I'm an artist, and in my fantasy world, all types of creatures exist. This standpoint has forced me to cross paths with this mystical land of drama and weirdness that the Furries call home.
Personally, I thrive in it. I troll as often as physically possible (not on the escapist, of course. You guys are cool, and therefore safe from my wrath). It's so easy and fun to do that it's almost a crime not to. That being said, trolling is not about hating. It's about the lulz. I don't hate furries at all. I just think they need to stop taking themselves so seriously.
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Now, I passingly dabble in psychology, so I apologize if my ignorance offends someone more well-versed than I:
I find the Furry fandom as a whole to be an utterly understandable/normal psychological phenomenon. There are so many factors that could open a person's eyes to socially acceptable aspects to the fandom. If you ever enjoyed an anthropomorphic character on TV as a kid (or adult), you already know the draw.
What separates you from what I'd consider a true furry is this:
Even if you (a non-furry) fantasize about characters with animal traits, or about having them yourself, fantasy is fantasy. It doesn't go any farther than your imagination and comfort zone allows you to take it.
With a furry, they really believe their fantasy goes farther than that. This can be for several reasons -- Maybe they were tormented teenagers who found the subculture during an "I hate humanity(everyone)" phase. There are more religions with animal gods/spirits than there are monotheistic religions (Christianity based or otherwise). This makes Spirituality a readily available means of defending this mentality.
"Humans are disgusting destructive creatures so F**K YOU I'M A DRAGON!" one might say. Whether or not this mentality is the majority rule, I have no clue. I've met both this type and reasonable types of furries in relatively equal numbers.
On the other hand, anyone that says this is a fetish based fandom is either trolling for a flame-war or extraordinarily misinformed. Humans are naturally sexual creatures. Sex is an integral part of our social makeup as a species. If a person believes themselves to be in part or in whole another race on the inside, it's only a matter of time before they begin to sexualize the subject matter they identify with. This is a clear indication that the fetish came after the fandom.
This does, however mean that no matter what anyone claims, if you visualize yourself as non-human, you do or will sexualize it eventually. There is no way around this unless you happen to be asexual (celibate by nature).
Anthropomorphism of any kind has this same limitation. If you give an animal human characteristics, sexuality will eventually come into the equation. If you think about it, this is a proven truth. Think back to your cartoons; Do you not remember female characters "turning on" the male characters? Even in innocence, this connotes sexuality. It's only a stroll around the corner from "fox guy boning Mewtwo."
Either way, whatever floats your boat, as long as it doesn't infringe on other's rights. Just don't act so amazed when someone calls you out on your cub-tentacle-rape-scat fetish 'cause you were too stupid to keep it to yourself.
Edit: By the way, I forgot to mention something important; The true definition of a fetish is a sexual deviation that is required for sexual arousal. In other words, for it to count as a fetish, it must be necessary for the individual to become aroused. E.g., a foot fetish literally means you only find feet to be attractive. This is not psychologically normal and it obviously isn't a fair label for most furries.