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Consider an earth-like world without any flying species.
What could be the possible (I'm looking for a physics or chemistry/biology answer) cause of this?
Set aside trivial solutions as "random mass extinctions" and so on, I am willing to accept an answer that especially targets flying beings.
The following stretch what you mean by "earth like" to the fringes of our world, but might be doable.
We know that some birds -- penguins -- went flightless in order to swim better and eat fish, near the Antarctic. It is plausible that an ice planet, with most of its behavior happening inside the oceans, penalizes flying beasts too much relative to the amount of additional food they can get. The only organisms that survive outside of the ocean are those which live in burrows in the ice and hunt in the ocean, making it terribly inefficient to fly.
The magnetic field is weaker, the planet is heavier and drier, and the sun is perhaps bigger and bluer and we are a bit further out to compensate. This is a very speculative possibility of tweaking a lot of different parameters a little bit to get a similar-but-very-different Earth.
The idea is that the candidate atmosphere has a much weaker ozone layer and is more transparent to carcinogenic light -- UV, X, and gamma rays all have photon energies which can break typical chemical bonds. However, there is a possibility that this is mediated near the planet's oceans and surface because the surface is heated a bit more than Earth's usually is (which requires a bit more gravity) , causing air currents to be much stronger and storms rage over the planet.
The idea is that the experience "on the ground" is one of a perpetual smoggy haze mixed between fogs and dust, somewhat obscuring direct sunlight; the hope is that this provides protection from the carcinogenic radiation close to the planet's surface. There would still be sheltered places -- caves, canyons -- which see the development of flight, but it would no longer be a worldwide phenomenon.
So this idea is to hit the birds and insects with a triple or quadruple whammy: yes you can hypothetically fly but (a) you'll be more likely to get cancer and (b) you'll not be able to see your prey and (c) you'll have to ground yourself for cover anyway when the daily hurricane blows through and (d) your bones have to be even lighter and more frail to resist the extra gravity.
In response to these, perhaps flying per se is no longer a common design goal, but perhaps gliding is more prevalent. One can imagine membranes like sugar gliders have, or one can imagine that lighter insects throw up a "kite" of spider-silk and "sail" to distant locations like spores and such do.
The first flying insects appeared (as far as we know) in the Devonian, some 400 million years ago. Before that there were no flying animals. So not only is a world without flying animals possible, our own Earth was such a world for more than 90% of its history.
The catch is that flight emerged as a life strategy almost as soon as there were animals living on land... And there are flying fish too. (Yes I know that flying fish glide.)
Discounting the problematic flying fish, flight has evolved 4 separate times that we know of.
Given that we are considering "an earth-like world" with similar gravity and atmospheric composition, there is one one common denominator to the 4 events, and that's evolutionary pressure/natural selection.
At some point it became advantageous for each species to develop flight, the ones who could glide and flap succeeded, the ones who could glide and flap and fly better than the others fared even better.
Other than evolutionary pressure there's no one thing you could remove that would stop flight evolving at some point, and if you remove that then evolution isn't going to happen.
You could say flight hasn't evolved yet, but consider the young spiders that spin strands of silk into the wind until the wind picks them up and moves them along like seeds, and some plants figured out how to glide a long time ago, "flight" is ubiquitous in nature. Given the number of things that almost fly (time to mention the flying fish here) true flight is only ever a couple of adaptations away.
Evolution of flight is an excellent source on the subject
Life will find a way . . .
Sort-of very thin atmosphere is a possible background for this scenario. Assume there is sufficient oxygen to support some life but it's too thin to support flight. Anyway, flight would demand much energy and a thin atmosphere makes it worse. Animal need a much greater lung capacity and that would make them heavier too. Don't make it too thin, though: Water's liquid state has a narrower range. At 100 mbar (1/10 sea-level pressure) water evaporates at 50c which is reasonable as most places on Earth are not as warm. Check water phase-diagram, in case your scenario involves water-based life breathing oxygen.
Wind-borne pollination is still possible, but flight is more difficult.
As other answers say, flight emerges due to evolutionary pressure and advantage. Since you can't mechanically prevent flight being workable, you would need to remove its advantage or have a recent and somewhat selective mass extinction that affected fliers.
For example, suppose that the terrain was such that a flier wouldn't benefit at all from flying, for some reason, then we can expect flight not to arise. Or suppose all fliers became ground dwellers due to giantism, or only ground dwelling fliers survived due to volcanism in the very recent past that specifically affected fliers above non fliers (due to toxins in the air that due to climate didn't reach ground level)?
The problem is, it feels contrived right now. I can't think what would make ground travel so strongly preferred as to completely remove the odds of at least some flier benefiting, or radiative evolution explosively reoccupying the niche. And global atmospheric disruption would have much greater impact than it sounds like you want.
Make flying so expensive that it's not worth the cost. For example, by very strong and unpredictable winds. But such conditions will significanlty affect all other life beings. Plants would be low and robust, animals either heavy or having always strong grip to surface or plants.
Higher gravitation would also make wonders. While it would not make flying impossible, it would reduce the size of the animal where flying is viable. I suppose you don't consider microorganism floating in air as 'flying animals'. Anything too small to see could be ignored in your storyline.
Hmm.. some thoughts:
a layered Athmosphere with a deadly layer in ca. meters high wich is poisonous or is not breathable. But this has other impacts.
SciFi Solution: Space-based system which kills anything flying (to prevent anything to leave the planet?)
Fantasy Solution: one flying Species (Dragons?) which kills any other flying creature.
since you asked for a biological explanation: what if there is a special biologic difference which leads to creatures that cannot move their arms/wings very fast? As far as I rmember, flying Insects and Birds fly by moving their wings fast - if you make that impossible, you dont have flying Creatures anymore.
All Ideas have great Impacts on the World, but maybe there is one for you..
If you remove flying creatures you will affect your planet's plant ecosystem.
Flying animals(insects) are very important for plant pollination and without it the plants couldn't reach the ecosystems outside their emerging points and as a result there wouldn't be a evolution of the plants by surviving in different environments and cross-mating with the adapted plant types. Every plant would be confined in a small area because of the lack of reliable seed transportation(insects) and a change in the environment would kill all this weak, non-evolved plants. It wouldn't be possible to have a stable life on this planet.
Some resources:
Bees Matter.
The importance of Pollinators.
Role and Importance of Pollinators.
University of Minnesota Research
Flying creatures have a great impact on the plant ecosystem and if you move them out of the equation through some scientific explanation, you should redesign the flora and the fauna of your entire planet from the beginning.
I think it's possible that in a flat world (no trees, no mountains, no hills) there would not be the necessary environment pressure for the flight trait to appear.
Think about it, most flying animals start first as gliding animals, that trait permitted them to save dips (jump from one branch to another) and escape from a predator. If no dips exists, there's no use in gliding, and as I see it, gliding needs to come first so flying trait can develop on top of it.
I saw a documentary, more or less realistic, where insects developed areas of the bodies with increased surface area to lose heat, then were able to jump further( proto-wings helping this) by "flapping" their proto wings, and a time went on, the wings were bigger and they learned how to fly. Perhaps your planet has no need for animals to lose heat?
If you consider removing atmosphere to still be sufficiently earth-like, then wings would not have anything to grab onto, propellers would not work either as they work by grabbing hold of air to create a push forward. The animals would need something like jet-engines or rocket pads to fly.
Now maybe that would still not be impossible since in fantasy and science fiction you have things like dragons who breathe fire and stuff. Maybe an inverted dragon species which farts flames which create a jet propulsion could still fly in such a scenario.
How many worlds do you have? If you have a large enough sample size, you'll see all sorts of worlds with individual anomalies. If this is intended to be one planet in galaxy-spanning science-fiction setting a la Star Trek, maybe it's the one and only world where no flying life forms are known to have evolved, just by the vagaries of natural selection not hitting on that particular strategy.
In a nutshell, the mechanism that targets flying creatures in this answer is "probability".
It could be an moon orbiting a very large planet with an ice layer on the surface and a salty ocean underneath like Europa.
It’s difficult to have animals and yet prevent them from exploiting an ecological niche without making your planet too non-Earth-like.
The physics of flying make it much easier for smaller animals. In fact for anything smaller than roughly insect size it become more of a challenge to not fly by being blown away. If you can prevent animals from being too small (I know not how) it will stop them from flying.
The ease of flying also depends on the density of the atmosphere. If the air is too thin, flying becomes impractical.
Trivially, if life could not exist outside of the water (cosmic radiation maybe?) then there could be no flight.
