Why do people always say "living your life well" is the ultimate revenge?

Because people are petty idiots who think active revenge is something good. ALL that proves is that you are still hung up on someone. When you just live well and DON'T worry about getting them back, you have truly matured and have shown that you can live better without them. This dis-connect then shows them that you have moved on and are a better person. Getting revenge is wholly indicative that you still want their attention.