I'm definitely secretive about being a furry (see: using a different browser for furry-related things, and not keeping an internet history). It's not so much a matter of being embarrassed, but more of a product of the fact that I'm generally a private person (my facebook didn't have a picture of me on it, even when I personally knew every one of the friends I had on it; I didn't give out my last name anywhere online for years).
I dare anyone who is secretive about being a furry to tell 3 of their friends at some point. Not all at the same time, just one on one if you can. I'm pretty sure you'll be surprised by their reactions.
edit: This becomes void if you mention yiff...
Yeah, no. The vast majority of my friends are, like me, the kind of people who spend a ton of time on the internet. It's not like I'd have the opportunity to frame exactly what a furry is to me, as they have preconceived notions. Most of them are fully aware that some people dress up in animal suits and then fuck each other/masturbate to feral porn/whatever else 4chan says is a common furry passtime, and will assume that I either do or want to do such things. Frankly, I just don't feel like having a moment anywhere near as awkward as that.
Note: I don't blame the fandom for any of this. I blame human nature (the "worst" people in any one group are almost always going to be assumed to be the standard by most people).