I tend to keep one thing in mind. (this is really only true in open discussions not some type of private messaging) Those you are having the discussion with are, 95% of the time, not discussing with intent to learn but discussing with intent to argue. The people you are really trying to convince is not the person to whom you are talking but other people who are reading the discussion with an honest interest and intent to learn. These type of people, however, rarely jump into the discussion because they fear they are not versed well enough in the topic.
Treat the argumentative person as if he is honestly asking a question (unless it is fully obvious he is just leading you off on tangents etc) because it is quite likely those that actually want to learn more have similar questions. Decent respect and avoidance of such things as ad hominims, strawmen, and the like will bring your argument more credibility as opposed to the person, such as you find in progressive circles, that will consistently respond with “Youre racist” or “That’s only what ignorant people think”, or (and I actually heard this one after I said that the individual could run their life better than the state) “Youre such an elitist.”
Secondly, on a more personal note, I tend to continue to engage in those kinds of discussions because it forces me to exercise my knowledge of a topic, to further develop debate skills and to think deeper into certain aspects of a given topic. If nothing else, those kinds of discussions prepare you for when you are actually engaged with someone who has an honest intellectual curiosity. I know this from personal experience. I was one that first was recommended Bastiat, so I read “The Law.” I realized that I wasnt the only nutjob out there that couldnt reconcile natural rights with the current state of politics in America from the “Conservative” or “Modern] Liberal” side of things. I read discussions likely like the one you are involved in without making my presence known