Tell her that online multiplayer games are the modern equivalent of team sports. They promote working together as a team, celebrating success or failure as a group, friendly rivalry, and promote discussion of shared events at school later. In short, they enhance your social skills rather than reduce them.
On the other hand, there's no chance of you getting injured or paralysed for life while playing video games. You're not hanging out god-knows-where with god-knows-who doing god-knows-what at all hours. She knows exactly where you are and who you're with and what you're doing, and that you're safe.
And if she raises the spectre of violence in video games please remind her that almost every boy in school plays video games, and that if there were any truth to that sterotype there would be blood on the streets every day and she'd be scared to let you go to school at all. Grand Theft Auto - one of the games singled out by nutjobs and the media for it's violence - sold millions of copies - it made over a billion US dolars in revenue in its first weekend on sale - more than any movie in history. If there was anything to worry about the courts would be full of murderers claiming that "GTA made me do it" and there'd be a world-wide outcry. Instead the fuss all occurred before the game was released, and was based on the opinions of ONE or TWO people who had never played it and seemed to think that viewing a few sexually-themed images would destroy young minds - images that were less risque than anything seen on Cable TV (or sometimes even regular TV - have you watched commercials recently?? - and the game features toons after all).
The truth is that the overwhelming majority of gamers are highly intelligent, high performing (games are goal oriented after all), and non-violent in the extreme (we're GEEKS for heavens sake). Most gamers are high earners too, and the majority are professionals (in my experience - nearly ALL my fellow computer programmers play games - some even build them).
I think limiting your game time to ten hours a week is one thing. Banning you from playing is hardly going to motivate you to do anything positive. Develop depression? Maybe. Lose a common interest with your friends? Probably. But nothing positive. Tell her you love her and ask her to reconsider for the sake of your social relationships and then work your butt off to prove that you CAN do well in school and play games responsibly. Good luck.