if you ask me, He's just speaking his thoughts out loud. It isn't that he is crazy or going crazy, it's just that some people like to hear themselves speak. Talking to yourself is also another way of relieving stress during overly frightening or angering moments. It's also a way to relieve yourself of loneliness, something that I used to do a bit. People who often talk to themselves quite often also have social anxieties that were caused by traumatic moments, in either childhood or during a crucial period of mental development.
You have to understand that Dante is not the most mentally sound of people. No, he isn't crazy nor mentally challenged, but he missed out on what he should have been getting as a child: Love, affection, and important key interactions with his parents and sibling. I'm going to go on a limb and say that Dante may in fact be a moderate sociopath, the way he acts and his childhood past leads me to believe this.