Actually, I'm not really sure. I think it started when I found my first Microgame from Metagaming (Chitin, a $3 sci-fi wargame about warring bugs). Liking what I saw (although I couldn't get anyone interested enough to play), I bought other Microgames, including Melee and Wizard, which became the foundation of The Fantasy Trip, which eventually led to GURPS.
And then there was this D&D thing going around high school in the early 1980s. Plus I played one session or two of Traveller. In college I found a TFT campaign, plus a little D&D, plus RuneQuest, Champions and Ars Magica (and Pendragon and Call of Cthulhu and on and on and on)
What led to this obsession? I think it tied into my newfound love of science fiction (mostly literary, with a little Star Wars, Star Trek, and Doctor Who thrown in). The idea of creating a shared imaginary world with rules and dice also intrigued me. And then, too, my Friday and Saturday nights tended to be free ...
"On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
- Charles Babbage (1791 - 1871)