A recent comment on io9 got my rage-meter up because of its use of the term "fangirl." I was clearly not the only one who found it offensive, and the OP genuinely seemed a bit confused and taken aback by the amount of heat his comment was generating, and several other commenters jumped in to tell those who found the term offensive that they were overreacting and to calm down. A few of the comments I recieved tried to equate "fangirl" with the term "fanboy," in an effort to make it OK. But here's the thing: Fangirl =/= Fanboy. Both are dismissive terms, but Fangirl has an extra component of misogyny to it that makes it doubly dismissive and offensive.
Both terms are used to describe a particularly obsessive sort of fan, specifically of scifi/fantasy. However, "fangirl" is also likely to be used to describe a female fan who is mostly interested in the physical attributes of the male actors in the tv show/film in question. The implication is that the "fangirl" is ONLY interested in the movie/show/comic/game because she has a sexual/romantic interest in the actors or characters portrayed. It's just another form of dismissing female fans as not genuine. The female fan isn't actually interested in the story, the world, or the themes in the way that a "real" fan would be, she just wants to fantasize about the lead actor. And while male fans are often accused of enjoying the sexual aspects of female characters a bit too much, it is generally acknowledged that they have an interest in the story beyond T&A.
Another comment that I received actually underscores this idea: The commenter stated that male fans can be fangirls and female fans can be fanboys. If there is no difference in connotation between the two terms, then this distinction is unnecessary. And calling a male fan a "fangirl" is likely to have the same implications that calling a man a "bitch" would have. It is both emasculating and misogynistic by implying that a) there is a fundamental difference in the way men and women react to and enjoy genre offerings, b) the male fan is acting like a female fan, and that c) acting like a female fan is bad/ not masculine.
A quick search of google and my own gif folder reveals a pretty thorough picture (heh. gifs make a picture) of what the term "fangirl" and "fangirling" truly means:
These images reveal a distinct sort of over-the-top, unrestrained, feminine excitement. It is clearly meant to be ridiculous. It is not the sort of thing a "serious" fan would do. It is based wholly in an emotional response. Let's contrast that with a few of the top results I get when I google "fanboy gif"
While these images are not complimentary by any means, they are not as monolithic as the fangirl images, even when one takes into account that many of the top results for "fanboy" images are gifs from the movie "Fanboys." The picture that comes together of a fanboy is one of a fan who is obsessive, perhaps overly so, and nit-picky. They also reveal a particular kind of fan who holds up his particular fandom over all others, someone who plays a kind of fandom zero-sum game: any admission that something else has value somehow takes away from the fanboy's particular obsession. While this is not seen as a good thing, it doesn't carry the same dismissiveness and derisiveness as the fangirl images.
I have no problem if women want to call themselves fangirls, just as I have no issue with women who claim the term "bitch" for themselves. But these terms are highly loaded and can be derisive and should be used with caution. Unless you are a part of the group of people being ridiculed, I suggest recognizing that fact, backing off, and not using it.