Let me preface this by saying I've already finished the piece this question is about but I'm wondering if I missed something in my logic so I want to see if there's something you see that I didn't. The basic question is for what tangible, material reason or reasons (so not matters of philosophy or just "how evil can we be today?"), would a star system, that isn't doing badly and isn't overcrowded, invade another star system that is no better than their own? The system they attack has the same number of habitable worlds, same survey numbers on quality, and quantity of raw materials, same standing population. Especially is there a reason to attack a system that isn't better than yours in such a way as to risk the habitability of it's only terrestrial world?
The basic question is for what tangible, material reason or reasons (so not matters of philosophy or just "how evil can we be today?"), would a star system, that isn't doing badly and isn't overcrowded, invade another star system that is no better than their own ?
Greed is about the only reason that makes sense. Maybe ego.
The system they attack has the same number of habitable worlds, same survey numbers on quality, and quantity of raw materials, same standing population.
The reason one group attacks another come down to six things :
Desperation - They have something you need (or will need "soon").
Greed - They have something you want (but don't really need).
Ego - Someone in charge can insist this happens and their ego is linked to how much they have control over. The words emperor and monarch comes to mind.
Cultural Xenophobia - They are "they". You just hate everyone else.
Fear - For whatever reason your culture fears the other one. This could be legitimate fear or fear based on incomplete or poorly interpreted knowledge or a cultural victim complex due to historic events.
Revenge - Payback time ! :-)
And typically it will be a bit of all of them.
Especially is there a reason to attack a system that isn't better than yours in such a way as to risk the habitability of it's only terrestrial world?
This depends on the motivation for the attack. An ego trip or cultural xenophobia would be at best ambivalent about destruction, and at worst keen to make it happen.
A fear based attack could be carried out ruthlessly simply on the standard military logic that once you start a war, don't think you can limit it, because you usually can't.
If you're desperate or in need of something they have then this may limit how much destruction you're OK with.
Assuming your civilization has advanced to the point where interstellar travel is difficult, but possible, I would consider some of the reasons behind European conquest of the Americas and West Indies:
Not as in outer space, I mean room for habitation, agriculture, industry, etc. Europe consists of a finite amount of land . If the available cropland is already in use, but we know of more land across the ocean where establishing sugar plantations will be profitable, why not take that additional land for such purposes? The available land in your solar system will eventually be used up, so risking a land war could happen if there is enough economic drive or your society believes it is at risk of exceeding the system's carrying capacity.
Typically this would be mineral resources. Historically, Spain et al. discovered gold, corundum, etc. was abundant in the New World (but probably not enough to constitute an entire city). It would be profitable to take control of any neighboring resources, especially if these resources were nearing depletion in your solar system. You say they have the same quantity of raw materials, but there's always
stealing claiming the resources the others have already exploited.
Going hand-in-hand with the last reasons, not only is it profitable to conquer, but it is also a show of wealth, power, and probably pride as well. If you successfully conquer the other solar system, some hypothetical third civilization is not likely to threaten you if you control double the resources, manpower, etc. In real life, imperialism occurred over and over throughout history. Assuming your people are human, or very human like in thought and logic, it is not a habit that will die easily.
Who knows, perhaps your neighbors in the next solar system over were going to think of these exact same things. Better if the fighting take place over there, threaten their civilians and their economy, not yours.
The reasons for war and (attempted) conquest do not need to be reasonable. Quite often the reasons of war and expansion are purely ideological or structural.
Was the German Empire just before WW1 overcrowded? Germany had the largest territorial extent ever! Did it lack access to raw materials or to world markets? No, it was one of the largest exporters and had already achieved a position of technological excellence. Was it poorer than its neighbours? No way, it was much richer than Russia (its neighbor to the east, there was no Poland at that time) and about as rich as France. Was it threatened in any way? Nobody could pose a credible threat. And yet they were fixated on the "historic need" to subdue France... They lost.
The Ottoman Empire in the second half of the 17th century was one of the world superpowers, it controlled the Black Sea and the eastern and southern Mediterranean, it had vast amounts of fertile land in the Hungarian Plain. It did have an overpopulation problem in Anatolia, but that was only one province, and "overpopulation" in Anatolia did not translate to unmanageable numbers. Nobody could pose a significant threat, and all it had to do was to apply mild economic and judicial reforms and encourage internal trade and migration. And what did they do? They went and besieged Vienna, lost the war, and began the long journey to oblivion.
Towards the end of the 19th century several Western European powers, mostly the United Kingdom, France and Germany, but also Portugal and mighty Belgium, started a frenzied effort to gain control over African terriories; this was the scramble for Africa that created those magnificent borders with no relationship whatsoever with linguistic or geographic boundaries. There was no reasonable reason for this ill-fated effort; the "new" African colonies were never profitable (as opposed to the "old" colonies established for reasonable reasons), nobody ever even tried to make a case that they would be profitable, and the scramble did bring various European powers into conflict. Less than a century later the European powers abandoned all their African territories...
The best example of the power of ideology to launch unreasonable wars of conquest is the First Crusade. English, French and German kings and lords started a war of conquest in Palestine, at the very limit of their logistic capacity to project force, wasting vast amounts of treasure and blood in order to conquer some dirt poor but ideologically important towns and useless patches of desert. Had they just wanted to make war on Muslims they did not have to go to Palestine, since Spain was much closer; and, unlike Palestine, Spain would have had many advantages: it was at the logistic limit of the Arabs to defend, it is much richer and not a desert. But no, they had to go to fight and die in a place far away. The Kingdom of Jerusalem lasted for less than two centuries...
I can't believe resources would be a sensible reason unless it was a technology-critical resource so honking rare that you'd need to expend the cost of invading systems across interstellar distances to get it. (Unobtainium, anyone?) Honestly, I find that to be remarkably unbelievable. Some ultra-wealthy magnate may send in a mercenary team to steal some... but outright interstellar war? What could possibly be worth that expense?
I'm not even happy with the need to expand. I'm a fan of a phrase I coined, "technology dichotomy." As a micro-publisher, we were plagued with books about time machines that could be activated by bumping a button with your hip... or stories about babbage machines in a civilization that hadn't invented the wheel. The idea that you can be large enough to seriously fight an interstellar war but can't terraform a planet seems, to me, dichotomous. Once you can terraform planets, it's an issue of time + cost to terraform vs cost + loss to conquer. I'm no expert, but I suspect it would be cheaper to terraform every time.
Further, space would seem the very epitome of the easy way toward population control. After all, "space is disease and death wrapped in darkness and silence." I suppose it's possible to have bloated planetary populations that can't be spread out through terraforming... but...
It's probably much cheaper and far more lucrative for the arms dealers if we fight amongst ourselves.
That really only leaves two reasons.
Your official "I'm just out studying the pulsar" crew comes across an alien species and in a classic, "What? Open gun ports are a sign of PEACE?" moment blew away the theoretically hostile aliens, thereby starting an interstellar war. You'd think diplomats could work this out with an appropriate sacrifice of human virgins, but in the world of Sci-Fi, war is almost always the result.
Hate You Chaka!
My moving tribute to Deathworld II by Harry Harrison reflects one of the most primal urges of all (obviously) intelligent species... the desire to not like your neighbor. We hate the Klingons, the Klingons hate us, punt the diplomats, this is war, baby!
I can see one more reason: a distraction. Suppose a civilization is doing fine industrially and scientifically. There is no real shortage of resources, enough to provide for everyone to live a happy life in theory. In practice, however, this doesn't happen. Government is highly authoritarian, and economical and social inequality is increasing over the last (fitting period of time) to the point where a few rich folk live in palaces while many starve to death. Of course, people in power are not motivated to solve these problems.
Discontent within the population rises, and traditional measures to silence it with police batons fail. Every month more and more formerly loyal citizens are joining the opposition. Seeing this might result in a rebellion, government might decide that an external enemy is better than an internal one, and uses it's mass media to breed hate towards some other civilization that it expects to be reasonably easy to wage war with. Maybe even a diplomatic incident or two is arranged (or faked) to make it look like "they started it first".
This does not bring the population any prosperity whatsoever: if anything, their conditions get worse, and many go to war, never to return home. War drags on for a very long time, and the two civilizations, maybe once former friends, now seem to be bitter enemies forever. On the "bright" side, though, people who formerly were thinking about taking arms against the government, now see a new enemy, and find solace in unity. And the elites stay elites for a while longer, just as they wished.
Reminds me of something...
The causes of war and, therefore, of conquest can be summarized as power, resources and ideology.
If their power potentially threatens your power or sphere of influence. Perhaps not now, but why wait for the inevitable?
Their system has system your civilization needs, will need or just plain wants. Also, related to power especially their access to resources will place their system in galactic geopolitical ascendancy over your system. Resources can include living space. For example: We both need earthlike planets for habitats, theirs is the closest and easiest to reach and conquer.
"We hold these truths to be sacred, self-evident and the best thing since sliced bread." Our heinous, slime-covered neighbours don't. They're evil. We must crush their horrible system. And, of course, vice versa. We are horrible in their three pairs of eyes.
Ideology is the most complicated factor. It can be any cultural, political, economic or religious institution or factor. Usually, tied up with power and resources either directly or indirectly. It both amplifies and reinforces any decision to wage war.
These three concepts have general application. They are the underlying causes. The putative reasons for going to war may include something like a Zimmerman telegram or the invasion of Poland or crossing the Rubicon, however, the terrible triad is usually lurking there in the background.
People want more space and resources
Although the star-system you speak of is not overcrowded people always want more space, more room to grow. Also this civilisation has not got a matter generator so eventually that solar system would run out of vital resources like metal and silicon. So the civilisation will need more resources as it's population expands.
Lack of Empathy
Could be that the Alien race don't acknwoledge us more than local fauna in their plans for the colonization of the sector.
Like the situation when you are building your home in a little terrain and you dont give a second thought at the ant colony that is going to be removed.
Mayor powers could incite aggression to destabilize a sector under the influence of another empire to gain leverage or start a bigger hegemony.
Interstellar conquest will be far different from anything else that we have seen or done in history, so it really needs to be in another category. The energy, time, and resources needed to carry out an interstellar war will be so great that normal justifications we accept on Earth simply won't do.
Resources? Any solar system is overflowing with energy and material resources. The single moon Europa is estimated to have 3 times as much liquid water as the entire planet Earth, and that is one moon out of the 67 orbiting Jupiter, and not counting the other known moons, tens of thousands of asteroids or millions of comets (not to mention all the bodies in the Kruiper belt and cometary halo).
Energy? The sun expends more energy in a single second than the entire Earth uses in a year (much more actually). A Dyson swarm around the sun is considered the end port of a technological civilizations, and a Level 2 Kardashev civilization in a cosmic scale. (see the Atomic Rockets Boom Table in the link)
Living room? It is estimated there could be up to 60 billion planets in the habitable zones around Red Dwarf stars in our galaxy alone. That is like 10 planets for every person alive on Earth today, if we can only get there.
So what could inspire the need or desire for interstellar conquest?
Firstly, there could be some sort of existential threat. IF an alien race has the ability to create a Nicoll-Dyson beam or fire Relativistic Kinetic Kill Vehicles (RKKV's). It is obviously desirable to ensure that your civilization isn't suddenly struck by a literally world killing event, so some civilizations might be inclined to preemptively eliminate the threat.
The second reason might have to do with how the aliens think. Their motives are alien by definition, so there could be some reason or idea that makes perfect sense to them, but is totally baffling or undecipherable to us. This is sometimes called "Blue and Orange" morality. If this is the case, there are hardly any channels to appeal the decision.
So interstellar war is out unless there is an existential threat to the civilization.
Why do you assume all those premises? There could always be a reason but it might end up being very contrived with all those limitations. Generally wars are fought for resources and if they both have no material reason to fight then war doesn't usually happen.
But, reasons for things do not have to be logical. A religious reason can very much develop. The Convenent in Halo started their war with humans simply because the existence of humans can not fit with their religion. Of course, they also had material motivation because humans controlled planets with Forerunner artifacts.
Another reason might be that one of the 2 species just loves war. Bloodlust driven by a convenient plot point can be used to explain the war starting such as in Warcraft. Where the Orcs were basically brainwashed into attacking everything and did so without any logical reason to.