The insults never add anything useful to arguments and still appeal to the same basic things as insults alone, even if they are accompanied by logically sound arguments. And while they don't logically weaken a position, they can emotionally weaken it for those who recognize frustration reactions as a sign of weakness.

Rage and anger might feel powerful, but they actually betray a sense of a lack of control. Trolls take advantage of this because it's a sign they are getting to you. Plus it's rare that people respond to insults by agreeing with the one who insulted them and the times when they do usually involve an appeal to authority (where the insulter has authority to back up their position and challenging them can have consequences).