I think I sort of arbitrarily just made flying a super-difficult thing in my post.
For anyone who's curious, Catherine's take on flight involves the idea that elementalists are a reference point and manipulate their element with respect to that point of reference (themself). But since everything is relative, Catherine shifts her point of reference to the air surrounding her. Thus instead of moving the air, she let's the air move her. It's like instead of picking up and carrying a ladder (in which user moves object) she is climbing the ladder (object helps user move). That's what I meant by metaphysical in my post. I hope I didn't just make life super difficult for anyone who wants to fly, but like Catherine said, different people have different approaches, Catherine's approach primarily gives her the ability to hover, to not generate exhorbitant amounts of wind when she's flying, to not have to rely on what she's wearing (like a wingsuit), and to have very fine control of her position and velocity. Turbulence will still affect her though, like someone kicking a ladder when there's someone on the ladder. Bad times.
EDIT: There's a reason she teaches philosophy.