There are certain topics I don't usually discuss with people, like politics (as noted in Getting People to Vote). Sometimes it's because I don't have enough information to have an opinion on a particular topic, sometimes it's because I don't have any passion for a particular topic (a nice way of saying I don't care about that topic).
And sometimes it's because the other person doesn't really care about my opinion. Some people are more concerned with convincing you that their opinion is the correct one. Not only are they welcome to their opinion, but you're welcome to it as well. Opinions aren't facts, but they are certain that they are right. And you could be right if you'd just agree with them.
Politics is one area where that frequently occurs. Since we have two major parties it's very easy for your party to be right, and the other party to be wrong. Take a polarizing topic, like health care reform or the war in Iraq, and it's very easy to make them black-and-white issues. And that's a shame because those issues (and most others) are far more complex than that.
For example, how would one rate President Bush as a president. (I don't have an opinion on President Obama yet, since he's only been on the job for a year.) To answer that question with a simple black-and-white response would be to simply say "he sucked" or "he was the greatest thing since sliced bread".
But it's not that simple. Now, I think President Bush is a good man who tried to do a good job, but I don't think he had the skills to be a good president, and I don't consider that an insult. Most people who know me know that I have an extremely high opinion of myself, and I don't think I have the skills either. Personally, I think his biggest problem was surrounding himself with some terrible, terrible people.
And that's where the polarizing groups would try to convince me that I was "wrong." One side would argue that not only was he a great man, he was the greatest president in the history of presidents, while the other side would argue that not only was he a terrible president, he was also a spawn of the devil. And neither extreme group would welcome any disagreement to their opinion. They are right, you are wrong. It's just not worth the effort to discuss it with those types of people.
Of course, all of the above is my opinion. But you're welcome to it.