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.
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.