Hermione doesn't like flying. Everyone who knows her knows that about her. Some have speculated that she's afraid of heights. Others have speculated she's afraid of falling. Still others thought that her inability to get the broom to shoot up into her hand during her only flight lesson made her so angry and frustrated, she never bothered with it again. That last one is why she never took to flying herself, but it isn't why she doesn't like it in general.
No. She doesn't like flying because it seems like Harry has a near-death experience on a broom every year, and she's afraid that one day, it'll be an actual-death experience. In fact, she's so scared of that possibility that the boggart in third year didn't show McGonagall telling her she failed her classes, it showed Harry's broken body lying on the quidditch pitch. She only tells people it was McGonagall because she knows that's the kind of thing people would expect a boggart to turn into for her, so it doesn't sound like a lie.
When Harry finally hears about this after the war, he wants to alleviate this fear of Hermione's, and the anxiety that comes every time he mounts a broom, if he can. If he can't, then he might just give up flying for her. Flying isn't as important to him as eliminating a source of anxiety in Hermione.