Squall starts off as many orphans would, being a loner that has come to learn how to rely only on himself and keeps people at an arms distance. The inner monologue stuff is there to take place of what he would be saying if he was a more outgoing person. If you actually play the game and pay attention to his character growth, you'll notice that the monologue goes away as he learns to embrace the friendships of his team and comes to open up emotionally. He starts off as cold, callous, and aloof, and ends up as a strong leader that is open and friendly. Shit, the last shot of him in the game is him finally smiling.
It's an incredibly good character growth story that gets really overshadowed by all of the weird bullshit the game puts into the plot.