When you're not telling the whole truth, you're demonstrating the quality of insincerity. You might detect a politician's insincerity during a speech, and decide to vote for his opponent, who seems more honest.
If you can't stand insincerity, you'll bristle when someone compliments your haircut in a false, overly enthusiastic way — you can tell they're not being forthright with you. Sincerity, the complete absence of any pretense, comes from the Latin sincerus, "whole, clean, or pure," or "genuine." Insincerity adds the "not" prefix in-, resulting in a meaning of "not genuine."