The problem with flying and growing at the same time is that flight is very tricky and controlled flight is nearly impossible. But it is not completely impossible, as long as you get everything absolutely right. Having different parts growing at differents rates is just not going to allow you get off the ground.
Another little issue is that flying models are not scalable. If you were to tripple the size of everything in a helicopter, then you'd end up with something very dangerous. The only good news for potential passengers would be that it most likely wouldn't even be able to take off.
Looking at teenagers it is clear to see that growing is slightly uncontrolled process that may produce a swan in the end, but there is a long period of being an ugly duckling.
And speaking of swans have you ever noticed that small (young) signets don't fly.
In fact the same goes for all birds. They wait till they are the same size as their parents before flying! This is in contrast the ability to walk. For example a lion cub can run and jump even though it is much smaller than its parents. The dynamics of the walk of a lion cub are slightly different to that if an adult. But not fundamentally.
Also insects can't fly and grow! A fly will start life as a maggot or grub, then turn into a pupa and after that start to fly. By the time a fly flies, its growing days are over. Sometimes round the house, mostly near the rubbish bin, I see small flies that, to me, look just like miniature versions of the common house fly, well I can be sure that tiny ones are not the young of the larger ones. They are in fact a different species.
Bats are another fine example, their young they are cared for and fed by their mothers until they are ready to fly, by which time the growing will have stopped!
If an animal were to try to fly and grown then the growing rates of different body parts would need to be very precisesly governed. Also subtle changes in wing shape would be required and timed perfectly to deal with the altering body mass. A big ask.
So in summary:
- a controlled walk is not tricky and is more or less scalable so you can walk and grow.
- a controlled flight is very tricky and it is not scalable so you cannot walk and fly
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