I guess it really all depends on how open your parents are and how old you are. I never said anything to my parents till now really (I'm 26 now.) Though I still don't think they really get it. They are just happy I'm doing something with my art. My parents don't pay to much attention to the furry fandom, and I'm glad of that. But sadly to tell you the truth, most of the fandom is a giant fetish. Though the good people who are into the fetish do keep it under raps. But it's like any group, a few will ruin it for the whole.
As for not letting you go to your first furry con, I see where he's coming from. He's being a good dad, that's all. Sometimes to make it easier on parents it helps if you go with close friends, or one of your parents go with you. Yea they would be embarrassing, but it makes them feel better to make sure your safe. My first convention was an Anime one, I went alone and didn't spend the night. Your age also plays a major part, if your a under 18 you really have no choice in your life really. Besides anything can happen at a furry con. Experience is on my side. (Heck even at a fur meet, Oh god there was only a curtain between rooms!!)
Sadly there isn't much you can do to prove to him once his mind is set. It's an unknown thing, and humans by nature are a fearful race.
I pretty much waited till I was old enough, had my own money and my own car. Parents can't really stop me then. But that's just me.
Maybe to help your situation you could try to make your dad more comfortable with the idea of you going off to a place full of potential perverts. Do your research, find out what ever you can about this convention (which one is it BTW?) And find people who have con to this con, ask them questions, how safe is it? If need be where is the closest emergency place? Also see if you can convince a close friend to go with you, more friends you have the more comfortable parents are. You're always safer in groups. If all else fails see if one of your parents or relatives is willing to go with you. Nothing says safe like family.
This article might help, I was there that year, the skunk they are talking about is a friend of mine. It was my first furry con, yes we had an incident. One of my friends ended up in a situation he shouldn't have. I regret not being able to help him out, when he needed it. So yea stuff can go down, but if you stick with familar friends you are normally okay.
http://www.hartfordadvocate.com/article.cfm?aid=3873I hope I help you out a little. Just keep in mind, you may have to wait a few years, and you're dad may never come around.
*Snugs* Hope it turns out for the best.