I have no problem with anime per se at all --- but I dislike almost all of its regular sub-genres. From shojo to hentai, the normal stuff of anime, particularly too much kawai, and anything which is basically a soap opera about character relationships at its core, leaves me cold.

But I like it as a medium - and I like Miyasaki and lots of the other thins you mentioned. But I'd never describe myself as an anime fan, even though I like quite a few specific anime things.