My brother had COD4, absolutely loved it. Can't seem to remember if there was much blood. Or cursing... I just remember parts of the Campaign Mode and Online play.
Some parents have reason to be concerned. The ESRB rating is really an outline though, if you ask me. It should be up to the parent whether or not their child can handle certain M rated games. If your get into a lot of fights, have anger issues, an obsession with guns, and plans for a bomb under your bed I don't think COD4 is the game for you. But a pretty normal child can handle it.
Revolucion makes the best point. You don't need to think up corny reasons. Try telling her you're responsible, you won't play 24/7, and you won't be brainwashed by it. I don't know why, but shooter games are just plain fun. So is Mario, but it is a different kind of fun. Just because I like to shoot virtual people in a game doesn't mean I like to shoot real people. I hate violence, but love shooters. Just start by telling her why you want it, and try not to use "All my friends have it". Fill that part in with "And it enhances my social life." >.<;