I think the biggest thing about "coming out" as a furry is that it's really not necessary. Yes, you can be proud of it, but there really doesn't need to be a time where you tell anyone if you really don't want to. Don't feel pressured.
If you do want to tell someone, don't treat it like it's weird. Explain it simply, and say why you like it. True friends will understand and most family members might. Everyone likes different things, and that's okay too.
However, if someone thinks it's different in a bad way, seems uninterested, or just doesn't care, don't take it offensively. Not everyone will understand and not everyone will be as eager as you are. Just brush it off, remember that it's normal to be you, and don't worry about it.