Although my family didn't fund my helicopter training, my dad did his best to talk me out of it: he works in the Forest Service, flies in helicopters all the time, and has known a number of people who have been killed in helicopter accidents. (In fact, my little brother is named after a helicopter pilot who was killed in a high-DA crash in the Gila Wilderness.)
Once I had my PPL, though, he couldn't have been prouder. He saw how important it was to me and from that point on was 100 percent supportive. He even let me take my little brother up as my first passenger...
If this is truly something you want to do, you might just have to suck it up and make it happen on your own. Once your family sees your commitment, hopefully they'll come on board, literally and figuratively. As you progress through your training, you'll also pick up some knowledge and experience that will be helpful in pleading your case (for example, my dad was really relieved when I explained to him how helicopters are able to autorotate).
There are ways to mitigate the risk of flying helicopters, and attitude and good training are two of them. If you're personally committed to operating safely, your family should pick up on that, and that will ultimately be more convincing than any statistics.
Good luck!
Elan