I personally don't think a FPS "teaches" violence, FPS's, except a few, simply contain violence.
There may be a slight hint of violent influence among those player that come from such a family where the proper values of life and reality were not taught to the child.
My daughter is six, and already we have conversations with her about movie and television shows (not games yet). We convey to her that what she sees is no more than stories like from a book, and that the people are simply actors/actresses playing roles to deliver the story to the audience (like she does in dance). We also spend a lot of time teaching her to be courteous and respectful of all people, that all things are special in their own way, and to always look for the good in everyone/everything. And, yes, apart from this online world, where i'm an ass, evil, and hateful of all of you (which was probably once my real life way as well), I am a totally different person in the teachings of my daughter.
Although to the weak of mind there may come some negative influence from violent video games, there are greater positives to the well rounded (not like in fat) and well brought up person. Organization, coordination, structured thought processing, quick reactions are a few of the positive things gain from FPS games. I'm sure there are many others.
If you have taken violence as your lesson from any video game, blame your parents. They did a poor job of raising you.