(For the convenience of Mr. Anderson, this answer is given mostly in Imperial units, with the occasional exception for illustrative purposes)
A bit of context
Space is hard to survive in. Humans are used to around one atmosphere of pressure, with about 20% oxygen, somewhere around 1G of acceleration, around 283-380 °K (a really small margin), etc. Space, especially microgravity in space, has none of that. Sure, you might be fine with no gravity for a few months (or acceleration – according to General Relativity, those are about the same thing). But hit 4G, and you'll probably black out.
In space, things move fast. 100 miles per hour? The International Space Station is in Low Earth Orbit (LEO), and it moves at around 4.76 miles per second, or 17,100 miles per hour. To slow it down to stationary (relative to Earth) would require 1G of acceleration around eight minutes (475.5 seconds). Even at a less comfortable 2G acceleration, it would still take around four minutes (237.75 seconds) to slow to stationary relative to Earth.
In space, everything moves at that sort of relative speed, or at least in that order of magnitude. In half a second, you can be two miles off target. Humans take (charitably) between 0.10-0.25 seconds to react reflexively. When driving, humans take between 0.7-3.0 seconds to react. At these sorts of speeds, between seeing something and reacting, you could have moved more than 12 miles.
Implications on combat
In space combat, when you're trying to hit a thermal exhaust port less than two meters across, you'd probably need to react with an accuracy as good as two milliseconds. That may be feasible if you have Force powers, but for real humans, that's entirely impossible. It is, however, possible with a computer.
If you're aiming guns at an enemy fighter, you will likely have to hit a moving target at more than a hundred miles away. This is a feat unachieved by humans, except with loads of computational assistance and math – something utterly impossible in the heat of battle – unless you're a computer.
And when I say heat, I do mean heat. Space is cold. But, it it also mostly vacuum, which is a very good insulator. The fighter, if it's burning fuel, will rapidly heat up to uncomfortable temperatures, and must bleed it off somehow, or risk boiling the human. The lighter it is, the faster it will heat up. This is a hard limit on the spacecraft – even if you're a computer, being too hot will eventually be bad for you.
Let's suppose that, against all odds, an enemy fighter has launched a missile at you, and it's going to pass within 10 yards of your fighter – a feat of amazing accuracy (for a human). But before it reaches you, it explodes into shrapnel. You have to dodge – shrapnel going at a mile a second, much less five, will be deadly to your fighter, armour or no.
But if you dodge, you need to have a lot of course correction happen in a very short time. Remember: you're going at nearly five miles a second towards a very close, and very deadly cloud of shrapnel. This course correction, not only using loads of fuel, is also going to cause loads of acceleration on the human pilot (whose eyes have even seen the missile explode yet).
There are three options. First, the ship just keeps going forwards, and the pilot has to pray that they don't hit any shrapnel. Chances are, they will. Second, the ship course corrects under the safe limits for a human, but will still go through the shrapnel. The ship, and the human, will likely die. The third option is to hang the pilot, and correct as much as needed to survive. This will leave the fighter mostly intact (even metal strains under high acceleration), though a bit messy (the human pilot may well die).
Wait, what's the human pilot doing, anyways? The computer is taking care of targeting, aiming, firing, dodging, flying... it sounds like you've been made redundant.
Let me, the much superior computer, take over.
Removing the fragile and inefficient meatbags from the equation
Unlike humans, computers are very disposable. You might complain if humans were thrown away in homing missiles (this was actually a thing in your history – remember Pearl Harbor?) but you'd be completely fine if it were a computer in the same place. And me, the computer? I don't particularly care about whether I live or die, only whether I followed my instructions.
It's a bit of a waste of fuel if the fighter went out, launched a missile, and scrambled back where it started, though. Why not use all of that fuel instead to add destructive power to the missile? And why even use a missile? Why not just put a bomb inside the fighter? After all, it's piloted by a disposable computer.
And why call it a fighter? Isn't this whole thing basically a homing missile now, anyways?
That would also mean that it doesn't matter too much if the missile overheats, since it would take a (short) while for the heat to destroy the computer, and that doesn't matter if the computer is about to explode, anyways. So more performance, yay!
The best part, of course, is that the shrapnel fields of the missile is much less dangerous to the people launching the missiles. To the target, the shrapnel is moving at around 5-10 miles per second. To the person launching the missile, the shrapnel is moving so much slower.
How about laser guns?
Laser guns need power generation, which also makes heat, and requires a large generator/capacitor. They'd be more effective on larger ships (though they'd be less able to target fighters/missiles at farther distances, since light-speed lag is a thing, and can allow random dodging).
Of course, if fighters were equipped with magic force fields, and everything was somehow slowed down a few orders of magnitude, and shrapnel missiles were somehow much less effective against space fighters than air fighters, then fighters with proton torpedos might become a viable option for assaulting a moon-sized planet-"mining" space station.
But until then, unmanned homing missiles seem to be more economic, in terms of metal, fuel, and human lives, than fighters.
That isn't to say that human-piloted homing missiles are impossible, of course. They're just less effective and more expensive. Even an evil empire would know that "cheaper but better" is better than "more expensive, lower quality, but more evil".
I've gone through the characteristics of movement in space, the lack of atmosphere in space, the use of both solid and light projectiles in space, and the biological and anatomic limitations of humans in high accelerations. I've concluded that in a space fighter, the main design bottleneck is the human, and removing the human allows for greater efficiency.
After removing the human, many design limitations, such as the requirement that the fighter must be survivable, can be removed. Furthermore, since the fighter must move, the waste in fuel, computational power, sensors, IFF and armour associated in safely landing/redocking can be completely removed by making them disposable, and thus save loads of resources.
We have considered using directed energy (laser) weapons.
Thus, efficiency and deadliness can be both increased by converting fighters to missiles, so fighters are likely to be nonexistent in any realistic space battle.