Sadly, the insults of those we do not respect often matter, because of what they imply about that person's future conduct, and because of their effects on third parties.

So for example if a bully starts insulting you, this may matter, both because this might indicate he is about to attack you, and because it may cause other people to turn against you. To give a non-cyber-bullying example, the insults of Idi Amin against Indians residing in Uganda surely mattered to them, even though they did not respect him.