Annoying pattern I

I write, on average, 6 blog posts for each one I type out and post. I engage people in debates almost constantly, either on message boards, on blogs, or in face-to-face conversations. I also surround myself almost constantly with podcasts, audiobooks, or TV shows like the Daily Show which feed my desire to comment publicly or at least write my thoughts and opinions down for later use.

As a result of a number of failed conversations I've had lately, I wanted to write down some generalizable patterns I have been running into. Perhaps some of you can help me to understand why this is happening, what I'm doing wrong in trying to argue my cases, or if this pattern is an inextricable part of being human, and I should get used to it rather than be annoyed by it.

The conversation goes something like this:
Opponent: Y is true.
me: I don't believe in Y, can you explain to me why you do?
O: Y is true because of X.
me: Now there's our problem. X is undeniably false. You yourself have admitted to me in the past/earlier in this conversation that X is [figurative and not literal/a patent falsification/extremely unlikely].
O: You're right. I don't stand behind X.
me: So do you still believe in Y?
O: Most definitely.
me: What is your reason for believing Y, now that we've established that X is not true?
O: Since Y is true, then X must have led to it, so X must be true as well.

Are people just appeasing me when they admit that X is false, or is it just innate to stick to our favorite lies, even in the face of overwhelming evidence against them?

Most importantly, please let me know if you've ever seen me pull the type of garbage that I'd like to critique in the next few posts.