There are a lot of different ways that the Internet screws with people's heads, but there is one potential component that I think gets overlooked. You interact on social media with a faint (or very sharp) awareness that you are potentially being observed by a lot of people. And being observed while in conversation with someone, or when arguing with them, can dramatically change how that conversation or argument plays out. So does your history and your intentions with that person. If you are arguing with someone as an equal in an attempt to understand where they are coming from, in the spirit of cooperation, you are going to try hard to hear what they are saying, and allow for a certain flexibility of definitions and understandings.
If you enter into that argument on the other hand under intense observation and scrutiny, you might be subconsciously putting some armor on, fixing definitions and understandings, and then white-knuckling whatever heuristic you have handy for understanding the world, because by golly you don't want to look like some lowly worm do you? Especially if you've been through previous fights, taunted and battered about by the enemy, and you've been steadily ground-down in daily life, your purchasing power and your personal efficacy steadily eaten away in a series of quiet humiliations.