Do you find it difficult to admit that you are wrong, and why?

I have started to notice that when someone disagrees with me or says something that is the opposite of what my answer is, I will instinctively say no.

The moment I finished saying no, I instantly notice that I had just done it again, I reacted instantly without really thinking.
When people actually prove me wrong, sometimes I will try to find my way around it to prove that, at the very least, I was not wrong and that both options are possible.

I do try and stop this or at least reduce this as much as I can, but so far I only notice myself doing this after I already failed to admit I am wrong.