This is magic, not science. Given what else magic can do, it shouldn't be hard to resurrect the dead, but we know for a fact that that's completely impossible.
There are rules and laws for how magic works that are difficult, if not impossible, to overcome. And these rules and laws do not always make perfect sense.
Besides, it's not like there's no canon precedent for it. It's outright stated multiple times that the most difficult transfigurations to preform are human transfigurations. In theory, if you can turn a straw into a needle, and a tortoise into a hare, then you can turn a human into a shark.
However, we know for a fact that they are not the same thing, and that human transfiguration is the highest, most advanced, and most difficult of all the transfiguration arts. I seem to recall it being stated that it isn't even part of the standard curriculum at Hogwarts (it's something like a special advanced class, or something), but I can't remember where I heard that, so don't take my word on it.
It's made very clear throughout the series that the rules and equations change drastically when humans become part of the process. Everything we've ever seen in the series that is meant to directly transform or change the properties of a human is either difficult to do, incredibly risky, extremely complex, or all of the above.
Polyjuice potion is one of the most advanced potions in existence, and incredibly finicky. Strengthening Solution requires several dozen extremely rare ingredients, and is considered (IIRC) a Class B Controlled Substance. And human transfigurations are the hardest transfigurations in existence.
Honestly, I have no problem at all with the idea that you can't simply slap a Levitating or Flight charm on a human, and expect it to work the same way it does for a broom or a floating deckchair.