When we are engaged in debate with someone, it is easy to think that the other side is stupid. Especially when you have thought about something a lot, possibly over the course of years. When you have so many reasons to think you are correct, so many corroborating pieces of evidence, how could anyone look at all of that stuff and not agree with you? They must be stupid!
Remember, the other side has likely done the same thing as you, they haven't come to their opinions in a snap decision, they have analyzed a bunch of stuff too (I guess not always, but let's consider a debate where both sides are knowledgeable). In fact, a lot of the time we have looked at the same evidence and come to opposite conclusions. This, to me, is where it gets really interesting. If we disagree on what a piece of evidence means, I like to really dig into it and figure out why. Where do we disagree, what are we interpreting differently, what assumptions are each of us making? What better way to change someone's mind than to really make them understand where you are coming from? Also, you should always be prepared to be the person whose mind gets changed. If someone has a really good reason that you never considered you should reevaluate. We should all be looking for the truth, no matter where it leads us.
One final thing I will end with, if you used to think one thing and now you think the opposite and call your opponents idiots, you are calling your former self an idiot. This should be enough to make you reconsider the insult. I'm looking at you /r/atheism