Let's say you enjoy talking politics, but one of your friends has an opposing view. Every time you talk politics, your friend gets heated and it always turns into a fight because they don't understand you, and you don't understand them. You don't talk for a week until you are both level headed. Eventually, you start to avoid talking about politics in front of said person and just focus on the positive nature of your friendship.
The internet scenario gives a nice opportunity to avoid this conflict. You can freely talk about politics and your friend doesn't have to be pissed at you. Instead of having to wait until your friend leaves the room to strike up a conversation, you can do so whenever you're in the mood under your alias.