Well, in my case, it's not that I make fallacious counter-arguments. My arguments are generally quite sound, and simple logic/rationality serves my need for something fundamental.
My issue is that, when something looks illogical on the face of it, rather than giving it the benefit of the doubt and try to imagine how it might work, I just shoot it down. And I shoot it down quite harshly usually, though almost always with a well-reasoned argument.
I have to be arrogant here and say that most of these arguments/ideas/statements I shoot down seem to really deserve it, which I know because I do sometimes restrain myself and just shut up and listen. However, sometimes my response is really undeserved, and I'd do better if I tried to understand where others may be coming from. Even if it's deserved, I could be much less harsh and argumentative, so as to better foster a good discussion.