I have the feeling that "furry fandom" goes farther than just dressing up as anthropomorphic animals, it usually involves roleplaying a "persona" (fursona for insiders) they invented. More often than not it seems to be familial/romantic/sexual roleplay that furries are most interested in, inventing families (mothers, fathers, sisters, etc) for their fursona, consisting of a network of other "people/fursonas" on the internet as a form of family roleplay. I personally think people interested in roleplaying a family with strangers on the internet is missing a family in real life.
I'm not a furry, have read a bit about them here and there.