Should Children (under 13) have Xbox Live?

In the time I've had LIVE, I've had very few instances of kids under 13 swearing like sailors. I play a lot of sports games (NBA 2K, FIFA, MLB to name a few...) I have yet to have a bad experience with kids swearing. However, when it's a violent game (GoW2, Halo 3, CoD) I always run into these guys. One game of Gears 2 my party had at least 3-5 instances of this happening. I even had a 10 year old saying most of those things you mention in your question. A 10 YEAR OLD!!! But to answer your question they shouldn't unless they can be actually mature enough to use the proper way. (Which will probably be never!!!)