Why does the media hate violent video games?

Because they do not know what a good game is.

Another point of view:

Blanket statements are problematic. If it is your contention that all media hate violent video games, it's incumbent on you to provide evidence. I've encountered media outlets that promote violent video games, which would belie your thesis.

But that's just quibbling around the outskirts of the underlying problem. Many people feel that current incarnations of interactive, first-person shoot-'em-up videos cause a desensitization to violence. Every time a disturbed individual shoots up a school yard and it is found that he was a fan of that type of entertainment, there is a misguided rush to ascribe cause and effect motives. While it may be true that sociopaths are drawn to this type of entertainment, I don't believe it can be conclusively shown that this type of entertainment causes sociopathy.

And yet, there are links. A while back, there was a movie where kids lay down in the street while cars zoomed around them. A few weeks after the premier, some kids tried it in real life and were run over. While you can't say the movie caused their deaths, it gave them the idea. One can only hope that stupidity isn't contagious.

Every generation feels that subsequent generations are going to hell. The people that laughed at the slapstick of the Keystone Kops were horrified by the Three Stooges. The Tom and Jerry kids grew up to be disgusted by the adventures of Itchy and Scratchy.

We're in uncharted territory here. The technology has improved to the point that the edges of reality are being blurred. We don't know what's coming next, and we fear the things we don't understand.