I understand flight from a mathematical point of view. I've actually read a few books on the subject, and I could explain how flight works to someone. However, I'm still fishing for an explanation that "feels" more satisfying though. Per the question, I still want it explained better.
EDIT: There's already a thread about flight. I asked the same question there, but phrased a bit differently: https://news.ycombinator.com/item?id=22993460
Put another way, weight pulls it down, thrust moves it forward, the resultant lift keeps it up, and drag limits its speed. Only rocketeers and fighter/aerobatic pilots need to really worry about the thrust to weight ratio as a constraining factor, because the vertical flight regime matters to them. From your average bugsmasher to your commercial airliner, it's not a factor (to the disappointment of pilots everywhere).
Consider that a Cessna 172 has a glide ratio of about 9:1, so it can go 9 units forward for every 9 of altitude it gives up. If that's hard to intuitively grasp, consider that it's traveling through a fluid. Surfing, even. The interaction with that fluid is why it works.
That any more satisfying?
I build this at school, using the same principle: https://no.wikipedia.org/wiki/Sivilingeni%C3%B8r#/media/Fil:...
But there is a tradeoff between force and displacement. Larger force = smaller displacement.
Same with a wing. The thrust force is lower than the lift force, but the horizontal displacement (velocity) of the wing is much greater than the vertical displacement (velocity) of the deflected air.
i.e. small force x large velocity = large force x small velocity