The question is one of diathesis. The fact that each of you and your local family have done well with video games is anecdotal evidence - that's the kind of evidence that may convince you, but has no scientific value, because not everyone has the same personality as you do. When discussing society's use of violent media, one must look at the effects on society as a whole, not on any one component of it, and that requires a lot of painful research spanning thousands of individuals and their perceptions.
Whether you specifically play/watch/enjoy violent video games/movies/sports shows means little. If permitted in society, these games/movies/sports are available to everyone in that society. You get them, but so does the creepy kid on the corner who's always talking about how awesome it is to hunt deer and miss vital organs so it bleeds longer. So does the scrawny guy sitting alone at lunchtime who hates himself, his life, and everyone in it - not just 'Emo Joe', plying for attention, but the real deal, Columbine style. So do the groups of teens hanging out in alleyways, talking tough about beating and killing because it's so much fun to pretend to be cool like gangsters.
The problem isn't what violent media will do to you - it's what it will do to people much stupider than you, people with serious mental handicaps, with criminal anger, or perhaps those whose brains were twisted in the womb when their mothers drank too much. Maybe normal people can sit back and enjoy violence, but it's these unfortunates who take the fantasy too far. Those are the people that watch the violence and are swayed by it, who find it acceptable or see it as a release from their problems.
Those are the ones who pick up the guns and shoot reasonable people like you. Guess what? There's no computer chip or special license to separate them from us. They get what we get. What the people who speak out against media violence want is to keep the media from people like them, not people like you, and they do it because they're afraid they will be the ones shot by the next idiot who believes that blood washes away regret. Since they don't like the games anyways, they don't care if society as a whole bans them.