She goes on common sense media. It says Half Life 2 is not for kids.
She also says I can't play games that have realistic people fighting, or if the game is all about fighting. She doesn't understand I need fighting games to blow off steam.
That's not common sense, that's fanaticism. OHMYGAWD MY CHILD MIGHT BECOME A MURDERER IF HE PLAYS GTA
Even though you don't start developing a sense of morality until you're around 16 years old. I played Perfect Dark, Goldeneye, and DOOM when I was a child and I'm no serial killer, I understand that it's wrong to kill. Common sense distinguishes reality from game, and any good parent would know that it's not the media that shapes their children, it's what they teach them.
In summary your mother is a crazy person