Well, then say "I know, cuz I'm not normal." xD
My mom knew I wasn't normal from the get-go so it wasn't a big shock to her; the way I said it was kinda in a conversation with my sister, it went like...
Sister: Man, I want some of those fuzzy rave legwarmers...
Me: Don't worry, my furry friends can hook you up, I know some that make em for cheap
Mom: You have some weird friends.
I guess that it helps that I'm into some other "weird" stuff like anime. She jokes around about my furry-ness, and she even offered to get me a tail at a fair, so I guess I had it easy, even though I'm a private furry fan.
There's also a thread about coming out being a furry, you should take a look because it also has some information on explaining the fandom stuff in it too.And if worse comes to worse, say that there's a game called Furcadia, and that its kinda like a furry World of Warcraft, and you wanna dress up like your character. (It kinda is, in a MMO sort of way...)
But you also have to see it from your parent's point of view... In Japan, there's a proverb that goes "The nail that sticks out gets hammered down", and that's what your parents are probably worried about. Furry is foreign to people, and in a world that's so full of hate, anything that's different could make you a target for persecution. People both verbally and physically harm gays, so they're worried about your well-being. (Not saying that being gay is the same as being furry exactly, I'm just comparing the two because in both, ignorance and misinformation is what drives people to treat both with disdain.)
And how old are you? If you're still living with your parents, you should have more priorities than getting a fursuit. Saving up for college, a car, a place of your own should be your top priorities. Even a cheap one will run you about $500, and even if you make it yourself, fur is not cheap.
In addition, where are you going to wear it? It'd be a waste to just wear it inside the house, that's like buying $500 shoes and stashing em in the closet. The only really accepted place to wear a fursuit would be at a convention that caters to the fantasy/anime/sci-fi crowd, and maybe at a furry outing, and even then its really pricy.
All that said, I'm not trying to dissuade you, I'm just trying to get you to think whether or not a fursuit would be the best purchase at this time in your life, its a big one, that's for sure.