Found this the other day. It summarizes well what types of arguments you will see. Online, when I've found someone that disagrees with something I stated, they usually fall into the bottom two categories: name-calling or ad-hominem attacks. Once or twice, I've seen someone "rise to the level" of responding to my tone (which is so very often sarcastic).
My personal agenda is to refute the central point.
If a person doesn't understand, then I will refute.
If they still don't get it, then I will make a counter argument.
Beyond that, if a person still doesn't get it, I know it is a case of ignorance, stupidity or knowing false-belief. At that point, there is no reason to continue communication.