To be right, in the "correct" sense, is such a warm feeling. It is a happiness. Why is it that so many people who have a "correct" stance on something can't seem to be happy until they that disagree can be brought to agreement? These thought fascists can be watched plunging into greater and greater despair while they with whom they converse resist them. Being "right" doesn't make them happy.
In my mind this is evidential. I suggest that this need to convince is rooted in their lack of security about whether they are, in fact, right. They know that they will feel more "right" if more people get on board with the idea. I have been asked, on telling someone of one of my more bizarre views, if anyone else agrees with me. Truth, thankfully, is not democratic. Vox Populi is not Vox Dei. Contrary to Romans 14:1, the compulsive who welcomes what he conceives to be the weaker brother for nothing but disputes over opinions is running a political campaign trying to gain by acclaim what his ideas did not have by merit. If he doesn't get enough votes, he loses.
Imagine if numbers or a movement was the arbiter of where you should feel the most ideologically safe. The broad way, where many went in, would lead to life and the narrow way, which few found, would lead to destruction. No, we should measure our ideas on epistemological grounds that do not include assent of our hearers. In fact, one of the reasons your insecure viewpoints fail you in those moments is that you had not bothered to convince yourself with proofs and so you had no proofs to offer. Perhaps if your ideas had merit in that they brought you a good and a happiness in just being believed by you, the very meritorious existence would convince the Philistines as they came into your life. It suggests this principle for wives of non-believing husbands. They will be "won without a word when they see the behavior of their wives."
As it says later in Romans 14, (regarding why you don't impose your views on the brethren but conversely be ready to pull your views out of the way for love) "The faith that you have, keep between yourself and God; happy is he who has no reason to judge himself for what he approves. But he who has doubts is condemned, if he eats, because he does not act from faith; for whatever does not proceed from faith is sin."
Remember Proverbs 9:12
"If you are wise, you are wise for yourself"