"Ignore" is good to use for someone who states opinions that you can't agree with, who seems to be of a different ideology than what you can accept, and who is also not directly assaulting you. Ignore people who aren't actually talking to you, if they are saying things you find idiotic. But if someone is openly quoting what you say and calling you obtuse, ignoring is not something you naturally want to do. The instinct is to strike back, but it's a good idea to let anger wane and then respond. The offender is not the only audience in an open forum. Ignoring can let his position stand unchallenged.
However, when it ceases to be an argument about something and turns into a tennis match of insults, that's when the conversation should go somewhere else.