OT: No, you weren't wrong to disagree with what she said, nor were you wrong to challenge her over it. That's the only way anything gets done, through a discussion of ideas and healthy debate.
However, you were completely and utterly in the wrong with how you went about it. Name calling and telling people to kill themselves solves abso-freaking-lutely nothing, and will only validate the opinions of the person you're attacking. It's simply bad behavior. And despite how you might think of yourself, it is very, very immature.
So I'm going to take a stab in the dark and guess that you're a pretty hardcore Fate/UBW, and that the franchise means something special to you. As such, when you saw someone criticizing it for being sexist, you took it personally and lost your cool. Okay, fine. I get it. Firefly is my favorite TV show of all time, and for certain reasons, it personally means a lot to me. And I also once came across a bugnuts article bitching about how sexist it was. And when I read it, my reaction was a great big pile of, "Are you fucking kidding me? What is this nonsense?"
Then I shrugged and went to do something else. You know why? Because they weren't worth my time. So what if some person I never met didn't like my favorite show? So what if they were wrong? It didn't affect me any, and certainly wasn't worth acting like an ass.
As for feminism, I do agree that those whole fit the stereotypical hardcore "feminazis" and "SJW" types are annoying, and do their causes more cause than good. But that doesn't mean all feminists are that way, or even the majority. It's just the radical, Lisa Simpson types are the most active online, while the rational ones with valid points to make get drowned out in the shouting.
My sister, for example, is a feminist, and it's something that's very important to her. Why? Because she's part of a field that's predominantly male, and her coworkers have been unintentionally sexist toward her. Not in an obvious "stay in the kitchen" sort of way, but condescending and sexist nevertheless. And we've had a lot of great discussions about it, and she also agrees that the SJW types give the movement a bad name. However, every single movement, ideology, cause, belief system, etc. has plenty of loud, obnoxious zealots. And more often than not, people tend to equate them with the whole movement and frequently point to them as a way to validate their dislike for that movement, while the rational ones unfortunately become casualties. So my advice to you would be to calm down, stop generalizing, and enjoy what you enjoy without worrying about what someone on the internet thinks.
EDIT:
Sung-Hwan said:
Yeah I give up. It's clear I melt down or can't cope with these topics, or get into how Western people think with their bias. The one thing I don't understand is how, even though the Escapist is a pro-Western site with articles mocking Japan, why are there anime/fan submitted VN reviews every now and then? The ones that are serious? That's just what I'm confused over.
But yes, if I am going to spend time on this site, maybe I should put on a facade of being a pro-American.
Erm, have you been in R&P lately? This site isn't exactly what I would call "Pro American."
On the whole, people are pretty fond of Japan and Anime around here. True, problematic trends and tropes get a lot of discussion and criticism, but we do that with just about every medium, in a "We love this and want it to be better," rather than "We hate this and it sucks!" sort of way.