Saying "full born witches" is like saying "full born engineers" or "full born republican." One is not born any more or less of a witch than anyone else.
You need to realize that you cannot force a person to accept proof or become supportive. Even if you show them positive proof of magick and give the most eloquent speech on how it is important to be supportive of your spiritual development, none of that will change anything unless they are open to it.
I know this sucks, but it would likely be better to simply keep it to yourself. I've openly been a magician since I was around your age but it's taken until now, ten years later and me not living with them, for my parents to reach a point where they could become more accepting and believing. Getting your family to be more accepting may need to be a long-term goal for you. In the short-term, however, it would seem most beneficial to just give them as few opportunities as possible to speak about magick. I'm not suggesting that you necessarily need to hide what you do, just that you shouldn't do anything to make it more noticeable than it needs to be - don't bring it up in conversation, wear your pentacle inside your shirt - simple little things like that.
You should also just keep in mind what a big deal it can be to go from a non-magical mindset to a magical one. Sometimes people have trouble accepting the idea of magic because all it implies is frightening. Their entire world-view may be at stake, and that's the sort of thing the psyche has a tendency to fight tooth and nail. There is a very real possibility that they may not be karmically ready to accept magick within this lifetime.
Don't let any of this dissuade you from trying to convince them, just realize that it will take time and there is a distinct chance of failure. At least the failure is theirs, not yours.