I just assumed it was a quirk. People are into different things. Some take it to extremes. And some of the fetishes are really weird or disgusting. I don't really want to know why they come about in the first place, it's like when the Todd from Scrubs thinks broccoli is hot. You just don't want to know.
I never thought of relating Birdo to furry just because, well, she's a dinosaur or lizard, she has no fur. But as I've become aware, furry can and does extend to any animal (lizards are known as "scalies" for instance. Or at least that's what one artist calls them). Pretty much anything that can be anthropomorphized seems to fall under furry. I've heard stories of inanimate objects coming to life and becoming part of this, which is easy to imagine if you remember Brave Little Toaster or anything with sentient inanimate objects.
As always, there's the argument that there's different levels of furry and that it's unfair to group them all together. There's some who simply prefer animal characters to humans and draw animals, like me. There's some who will dress into fursuits. Okay, kind of weird, but it's surprising how far they'll go with the costumes. I don't know where else you'll find costumes of Balto. There's some who pretend they're animals. Well, I guess the guy who played Gollum is okay when he does it, but this thing's starting to creep me out. Then there's the subgroup most people seem to think of, sometimes referred to as "furverts". Drawing porn or Yoshi+Birdo. Art quality and the bizarreness of the material is all across the board, but most of the time it's just really disturbing. It seems to be a well-known fact by now that the quickest way to disturb you is taking innocent characters you knew from childhood and... yeah, you know the rest. And then the people who decide to go even further than that... that's just too much.
Personally, I'm between "drawing animal art" and "fursuits". I never want to be in a fursuit, never felt the need to. By the way, I saw Yoshi+Birdo. That's just not right.
As for why a lot of people are furry for Birdo... heck if I know, I didn't know they were. Certain characters are targeted more. I didn't think Birdo was popular enough to warrant that, maybe she's just the popular one regarding the Mario universe. I've seen more popularity with Bowser and the Princess, which is still disturbing. I know Bowser's a villain, but come on, I grew up playing Mario, I don't want to see that sort of thing. Unless it ends up being a funny picture.
In ten minutes I'm going to wonder why I posted to this thread.
