People live with cognitive dissonance every day. It starts with our innate desire to live - no matter what, we are going to die someday, and there's nothing we can do about it. But we continue living without thinking about that all of the time, because if we couldn't we couldn't live effective lives.

In their same way, people want to believe they are acting virtuously, an idea advanced largely by the society that they live in. I can't admit that (for example) I genuinely don't give a fuck about the poor living conditions of people around the world that exist almost directly to drive my lifestyle, that by the standards of the USA are below average but by standards of the world are affluent. If I really had to care about that, I'd have to make really tough decisions and go against society to act on them. It's much easier to pretend that it isn't an issue.