Have you ever seen a painting, a building, a person, etc and thought, "I think that looks great!" or "I don't like this at all"? 

We often form opinions on the things we see and encounter, without ever understanding why that is. And then make up arguments for why we feel the way we feel. When those arguments are refuted, our feeling doesn't always go away, because the argument is usually not the cause of the feeling. It is simply something we thought the other person would find plausible for why we feel the way we feel. 

The process by which our brains make up such arguments unconsciously is called confabulation. 

And this is different from lying, because lying needs an intention to deceive, whereas confabulation has no such intent. It is simply how our brains work. 

When you're arguing with someone and they don't change how they feel despite you having refuted their reasoning for their position, it is probably due to confabulation at play. 

At such times, it is best to end the argument, because logic won't win.