In regards to what other people accuse you of, it's usually them projecting. In other words, the person who accused you of being an egomaniac could be avoiding fears that they themselves are being an egomaniac. Or the person who calls you a liar may secretly be afraid that they're not trustworthy.

Regardless, I've found experience to be the best teacher. I've learned not to be shy when it comes time to say "I told you so". It sucks, but you leave people the option to continue to underestimate you if you don't.