Impossible to say, really. I think the allure of "manbeasts" was always there, dating back to the Egyptians and older eras. People always respected the best traits and strengths of the animal kingdom, often drawing them into comparison with people. Fables and whatnot spread over the era, and there was a fascination the built up over time.

It probably just started to assemble more as communication became more widespread, starting with the infancy of newsgroups. Anthros were always there, evident in art and animation, and it built from there. The fandom itself got its basis on the newsgroups for those who shared a similar interest in 'funny animals" (we hate that term - it's so horrifically generic). It just sort of spread from the newsgroups to IRC and to MUCKs, and took off from there.