Unfortunately, our families can sometimes have a tough time accepting our social anxiety (not all families, though). Social anxiety is still a widely misunderstood disorder, not even completely understood by numerous doctors and therapists, so it also tends to be misunderstood by people who haven't even studied the disorder or who do not have a background in Psychology (like many of our family members).
Sometimes, but not always, the more that we get over social anxiety and start to get better, the more our family can empathize with us...but, this is not a guarantee. I know it happened with my parents, who used to not believe me or take me seriously when I tried to explain to them that I had social anxiety; when I started Dr. Richards' program and started to get better, my parents could finally see that I had a problem and I was struggling with it and that I was getting better from it. I know this also happened with a friend of mine who also used the therapy series and eventually this person's father, who was initially skeptical of them having social anxiety, started to finally come around and see that they had an anxiety disorder.
I think that sometimes other people can/will realize that someone has a problem when they see progress is being made, because they have a before and after perspective and can compare how someone is now than they were before. Of course, this is me speculating and unfortunately I don't have any supporting evidence of this; I only have my experience and other people's experiences to offer. Also, again there's no guarantee that the family of every single person with social anxiety will come around and become more understanding, as some people just don't want to accept things.
The best solution is to overcome social anxiety for you, and not for anyone else. It's challenging without the support with your family, I know because I didn't have my parents' support at first, but if you work on getting over social anxiety for yourself and do not care so much about the support of your family, then it makes it more worthwhile as you have a stronger feeling of self-accomplishment. And if your family does become more understanding, then that's a nice little bonus :).