I'd say because a lot of games (if not all) are a form of friendly competition. I'm not just talking about computer games here, even the most basic of childhood games has at it's heart an element of competition. Between two or more people these games result in both a winner and a loser, allowing both parties an even chance of winning. Between one person and an AI opponent the outcome needs must favour the human player, as success only matters to that one side. Therefore since the human element is playing - as it were - with a stacked deck, this results in a feeling of over-achievement or badass-ery.
Or because game devs are pandering to immature power fantasies. I'd like to believe my first reason had merit, but I have a sneaking suspicion that I'm talking bollocks and it's the second reason that holds true. In an effort to make my case just a little bit more credible I would point out that this feeling of 'I can take on the world' is usually only delivered in single player campaigns. Multiplayer games in which people play against people ditch the feeling of invulnerability in favour of making you just as vulnerable as everyone else, hence removing the feeling of badass-ery.