I have seen several posts in here about why Gamers have made Gaming such a crucial part of their identity, I cannot speak for all gamers but for me, it was like this.
In my youth, I didn't have many friends, my family moved around a lot, My Older Brother didn't like me (7 Years older, Brotherly competition and all that). So what did I do? I gamed. People made fun of me for being the new kid? Gamed. For being different? Gamed. People made fun of me for x, y, and z? Gamed. Throughout all the different parts of school, gaming was where I went to for relief, and in time, around the junior year of high school I found my school had a gaming club, and for the first time, ever. I felt like I fit in with something. Gaming, I dare say, saved my life. It allowed me to make the friends I needed, to grow as a person. To move on, many of those friends, without them I wouldn't have the drive to get up in the morning, And gaming is what tied me to them. I deal with work to get paid so I can go home and talk to my Girlfriend, and our friends about what we are gonna do that weekend for our D&D campaign, Or our Raids in wow.
So fast forward to now, 2014, Gamers are dead, Gamers are Rapists, Gamers are Terrorists, Gamers are Sexists who send threats. Rather than "Anonymous asshole sends Games Critic Threats", which as far as I can tell none of the threats Anita got were from someone she could identify, the first two of whom came from 4chan, which I will remind you, covers everything from Real Life, to Politics, to Anime, to Video Games, the threats from 4chan could have been bronies not gamers for all we know. The ones from Twitter, also have no way to identify them, and yet we are still called out for being the monsters, with no proof to back up that these people are even gamers... at all.
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I understand it can be hard to put yourself in my shoes and to see things from my eyes. But just imagine for a second, your favorite thing in the world, something that has literally helped you and kept you, and helped you make the friends you have, and cherish, who share their stories after a long day of work, about that awesome thing that happened. Imagine that they called Game of Thrones watchers Terrorists, because they sent G.R.R Martin threats about not finishing his latest book sooner. That sounds silly right? Surely they would just call it a group of extremists, or a group of assholes. Not the entire fanbase.
So if you, or they didn't mean All Gamers, then they should have used something else. A Sexist, A Rapist, A Racist. A Terrorist, Not gamers are rapists. Not Gamers are Terrorists, Not Gamers are Worse than ISIS. When they say Gamers, that means all Gamers, not magically some, and if you feel insulted it means you did something wrong. That isn't how language works, and it is another thing that shouldn't change to fit your needs.
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And finally, even if you do not understand why Gaming is so important to us. That is fine. You don't have to understand, Just understand this, or try to. We do not want women to feel like they can't game, that has never been the goal. We simply want you to stop trying to change gaming into a political thing. This goes for the men and women trying to do it. Gaming is about fun, When I play Total War I don't want establish a dynasty and conquer most of Europe (Or Japan) in real life, I play it for fun (Though there probably are crazies that think that playing a Total War game is good planning for the future, (It Isn't. The AI is crap at times))
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Edit - To the OP - Depending on who you ask, they want a lot of things, if you can honestly say to yourself you do not threaten people, you do not go around saying openly racist or sexist things, then you are better than the people who are decrying you for being as such. Find your friends, or make new ones, enjoy gaming.