The best answer here is the last one, that it allows the reader to sympathize with the monster. Before we hear his side, all we know is what Victor tells us and, by all accounts, the monster he created certainly lives up to his name. He murders his younger brother and is hideous. He chases Victor down and terrorizes him until he listens. This is all quite frightening, but reading the monster's perspective certainly changes things.
Through his narration, we discover that the monster only wanted to be loved and accepted like others that he sees. He is constantly rebuffed because of his appearance, the appearance that Victor gives him. Without this narration, we would continue to think the same way as Victor: that the monster is a terrible creature. But, because we are given a glimpse into the horrors he faced, we can't help but feel sorry for him because he is lonely and doing the best he can.
