Trying to change that seems almost like a slap in the face of all the women who did challenge the stereotypes (largely perpetuated by non-gamers, in my opinion) and play games for their own sake.

They didn't need handholding, a special invitation or games specifically targetting them.

I mean, my hand was held. The first video game I played was based on Star Trek, one of my favorite TV shows, for chrissake. If it weren't for that, would I like video games? Who knows? But that's how it went.

I want more girl gamers. If "more female characters" gets more girls into gaming, then that sounds good to me. I'm glad there are already girls who game, but I want there to be more. It's not really complex, right?

And the whole "slap in the face" thing is very abstract. That's not a strong argument.

I'm not condoning character judgements or attacks, It's just my opinion that they are becoming entwined with the actual debate

By GamerGate. Very deliberately. Obviously.

Oh, both sides. Okay. Whatever. We can get all "both sides" when I get you to admit that attacking the character of your critics is bad.

GamerGate supporters don't have a problem with attacking the characters of their critics. In fact, it is their first and most powerful response. This is a problem if your goal is coexistence.

Gamergate are terrorists.

In the sense of "terrorizing people", this is absolutely true. However, this is not the conventional sense of the term, so I would say this is inaccurate, although I understand why people say it.

Gamergate is a hate group.

I am not sure exactly what the formal definition of a "hate group" is, but GamerGate perpetuates hate toward "SJWs" and individuals like Anita Sarkeesian and Zoe Quinn. Yes, hate, not criticism. Like the "terrorist" line, I understand what they are saying, but I'm not sure it fits the conventional use of the term. But this one is closer.

Gamergate is made up of harassers.

I doubt that the majority of GamerGate supporters engage in harassment, but that is not what is being suggested here. (I doubt the majority of any oft-demonized group personally engages in the behavior that group is most famous for.)

GamerGate absolutely consists of many, many people who have harassed strangers on the Internet. Go look up the definition of harassment if you're curious what I mean.

Gamergate is made up of sexists.

Yes.

Of course, sexism is a large problem in the world. This is, really, an uncontroversial assertion when taken on its own merits. I would say a better question is, "Are the actions taken by GamerGate driven by sexism?"

Also yes.