Humans are emotional creatures. We don't feel emotions for rational reasons.

The emotion you felt is called cognitive dissonance. It's something that humans feel when they come to a point where one of their fundemental beliefs is threatened but they don't have good arguments to back them up.

I think it's quite valuable to have a strong reference experience of what cognitive dissonance feels like. It's make it easier to recognize the feeling when you feel it in the future. Whenever you are feeling that feeling, take note of the beliefs in question and examine them more deeply in writing when you are at home.