"It'll never last…"
"Someone with her background will never make a go of this…"
"Are you kidding me?" "Pathetic! Delusional!"
"Social media is a fad, the iPad is a toy, you're never going to amount to anything…"
Here's the thing about proving skeptics wrong: They don't care. They won't learn. They will stay skeptics. The ones who said the airplane would never fly ignored the success of the Wright Bros. and went on to become skeptical of something else. And when they got onto an airplane, they didn't apologize to the engineers on their way in.
I used to have a list, and I kept it in my head, the list of people who rejected, who were skeptical, who stood in the way. What I discovered was that this wasn't the point of the work, and my goal wasn't actually to prove these folks wrong, it was only to do the work that was worth doing. So long ago I stopped keeping track. It's not about the skeptics. It's about the people who care about, support and enable.
Instead of working so hard to prove the skeptics wrong, it makes a lot more sense to delight the true believers. They deserve it, after all, and they're the ones that are going to spread the word for you.