Materials. Birds can be relatively lightweight. People are relatively dense, as are our things.
Flapping causes damage buildup. Birds repair themselves over time, like any animal.
We have to control all those surfaces (feathers).
It’s easier to use the principles they use to glide, where the lock their wings, and do the same thing, but with thrust
Animals may have some very advanced designs guided by millions of year of evolution, not one of them has ever evolved a wheel.
If a bird had a key engine to generate wind for it, it wouldn’t need to flap either. It could just glide like a plane. Our planes are just better at doing what they are designed for than a hinged wing and I suspect if you tried it there would be huge forces on the joints and it would probably break.
A machine that flies like a bird is called an [Ornithopter](https://en.wikipedia.org/wiki/Ornithopter), and they already exist.
As to why they aren’t used more often? They add way to much complexity, and are way less efficient than fixed wing aircraft. As others have noted, many larger birds actually emulate fixed winged aircraft when gliding, as they use thermal air currents to fly for extended periods without flapping their wings, as flapping their wings uses way more energy.
We could, but we don’t want to.
Birds are made of soft and flexible materials. We build out of stiff metal. We could engineer complex mechanisms that replicate bird wings, but it would require a lot of parts.
The first rule of engineering is “The best part is no part.” Each little part needs to be designed and built to fulfill it’s function. The more parts you have the more effort needs to be put into making sure they all work together correctly. If we can achieve the same function with fewer parts, that is what we do, it’s much easier. Also when making the parts sometimes they are bigger or smaller than they should be. If you have one long metal stick that is a millimeter shorter than it should be, then that might be fine. If you have hundreds of tiny metal parts, each of which are slightly the wrong size those small errors add up. Fewer parts means less errors.
The next reason is movement. It is fairly easy for us to calculate a static part. It does not move, in some places there are forces pushing or pulling it, but those also remain mostly the same. If the part was moving in a complex mechanism, those forces would change all the time. Making it much more difficult to calculate if the part will do the job. Also the constantly changing pushing and pulling will make the material fail more quickly. Like a paper clip that you bend over and over, eventually it will break apart. That is material fatigue. It requires replacement more often, needs to be inspected more often, because we really don’t want airplanes to fail in the air. Inspections and repairs cost time and money while the airplane is not earning money by moving passengers or cargo. Fewer moving parts is cheaper and more reliable.
And of course comfort. Flappy wings would also mean the cabin goes up and down with each flap of the wings. While many people do enjoy roller coasters, an 8h flight of being constantly thrown up and down does not seem like an enjoyable experience.
There’s a [Smarter Every Day video](https://www.youtube.com/watch?v=4jKokxPRtck&t=70s) that covers one aspect well. While the feathers on a wing appear to form one solid surface, during the upstroke the main flight feathers individually rotate in a way that air flows through the wing. Kind of like Venetian blinds you open during the day and close at night.
Helicopters can do something similar when you direct them to turn (pushing air down on one side while spinning flat on the other side), but most helicopters have no more than eight blades on the main rotor. Compare this against birds that have over a dozen main feathers on each wing. The complexity needed to mimic just this one aspect is boggling enough.
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