First, I realize the limitations of this question which is why I worded it the way I did. I realize that you could easily find me a source of someone claiming this statement in some way and call it a day. This is why I phrased it as commonly asserted.
The reason I ask this is because it seems like a bit of modern historical revisionism. I hear statements from people like, "Well, they said man would never fly and they did, therefore X will likely happen." Of course, in addition to being a fallacy, is there any evidence that this was commonly thought in the first place? In my brief time trying to find any statements, I couldn't find anything along those lines except for modern sources of people claiming that people in the past said this. Are we looking at some "people thought the world was flat"-style revisionism here?
It depends on how far back you're thinking but given Da Vinci was at least theorising flying machines back in the 15th century, so even if people were sceptical it at least wasn't an alien concept. If you're looking for quotes it would most likely come up in works of literature or philosophy if at all, and therefore difficult to identify consistency. It is analogous to us today saying 'man will never teleport', or 'man will never travel through time', but we live in a technologically advanced society where man already has flown, and has already been to space- we have already broken boundaries so it is not so inconceivable we will do it again.