I never had a chance. I was steeped in SF and fantasy since day one, thanks to my family. Oddly though, Narnia escaped me, because my mother made us think it was something we ought to read, to become good Christians, and having a perverse streak, I wouldn't read it (being that reading is for fun, first and foremost, and moralizing is what Sunday School is for).
I also didn't read LOTR until I was in college, because I hated the cartoon version with a passion. Only my enduring love of elves and a desire to finally acquaint myself with some modern Christian writers overcame that.
And I hated Star Trek. Certain aspects of DS9 aside, I still hate it. And yet I've seen almost every episode of all of them save Enterprise, thanks to other family members.
All that, coupled with loathing for the Dark Crystal, and the wonder is that I'm still reading and watching SF&F. (The positives are actually too numerous to mention or remember. Star Wars is somewhat above all the others.) I like wild ideas, and other genres are too much like real life to invest a terrible amount of interest in. Might as well go out and live that life, if it could really be lived.
And I'm guilty of the cover art thing too. Not so much these days, but I still browse the shelves for things that catch the eye. The ONLY book in years to pass the other tests after the cover test (namely, reading the synopsis, first paragraph, and random page) was Angel with the Sword, by uh, Cherryh. And it was okay. I've mostly switched to word of mouth for my reading material now. Ironically an eye-grabbing cover on an unknown book now makes me suspicious, as it's a mark of mediocrity. But I still like pretty pictures for their own sake.