He was created as a character readers (young boys) could really relate to, which is a big part of his charm. Plus, when he was a teenager, it is realistic to have him moody all the time. I don't want to see melodrama with this movie, but Peter Parker is supposed to be a conflicted kid with shaky self-confidence. He was originally a nerd that gets picked on for Christ sake. Probably as iconic a cover as any for Spidey is this:
Beyond that, he is as much a hero as any other character when push comes to shove, but he doesn't always wear that part of himself on his sleeve like a Superman or Captain America would. The heroic "perched on a gargoyle" look isn't really what Spiderman is about.
