Easy to say when you haven't been the one suffering due to centuries of institutionalized misogyny that affects everything from the way you are expected to act, dress, to the career you can obtain and the rank you can reach, etc.
The problem with things like racism/mysogyny/homophobia/etc isn't just that racist/sexist/homophobic comments are insulting to a group of people (which sucks in its own right, but everyone gets insulted at some point, so no big deal); it's that these insults have been used for centuries as ways of putting groups of people down and painting them as unqualified to do certain things, or too stupid/crazy/weak/perverted/etc to function at the same level as other people who haven't been oppressed as much (mostly white heterosexual males). And by painting them as such, people have justified de facto discrimination for centuries, because these insults evolve into stereotypes which evolve into expectations that people in power can use to judge and oppress those without as much power.
In this example, the term is "feminist whore"; the term "whore" has a centuries-long history of being used to demean women who explore sexual options not considered the norm for females (implying that it's not right for women to sleep around as much as men, that it messes up their purity; something you still see to some degree in society today). So when you call someone a whore, all that connotation goes along with your statement; aside from just accusing the woman of sleeping around, you've used this word that basically implies that this woman has less of a right to do so that any man, that she should be having sex less because it's not right for women to want to have a lot of sex, that purity is being tarnished by her actions, etc. History DOES matter, because people have been using this word to tell women to stop having a lot of (and often any) sex, and it has shaped a society that still, to this day, considers a woman who sleeps around to be worse than a man who sleeps around (hence why there are so many adjectives for a woman who does it, and little to no adjectives for a man who does the same), and forces women to adhere to this constraint accordingly. By continuing to use the word, you still reinforce this history, even if all you want to do is insult the woman for sleeping around (which in and of itself, again, isn't the issue).
By attaching "feminist" to it like an adjective, it appeals to hated stereotypes of feminists (that they're awful mysandrists who don't deserve respect, etc). People think calling someone a feminist whore is funny because for decades most people painted ANY feminist (including the sane ones who actually want equal rights) as women who only want special treatment, who don't deserve to be treated any better than they are now, etc, to the point where when you think of "feminist," this is what you expect to get, even if you've never met one before. Not only that, but when someone says something about women's rights, people start to assume they are feminists, and they anticipate this sort of behavior even before the person has even had a chance to explain that they aren't looking for diminished male rights. That in and of itself is powerful stuff.
I will say that I don't think the example in this article is egregious enough to warrant widespread anguish and anger, and while it was completely unprofessional, I wouldn't say it was necessarily done with mysogynist intentions. HOWEVER, the notion that we can just forget about centuries of history, when that very history still profoundly affects the living conditions of many groups of people who still don't receive equal treatment, is a willingness to be willfully ignorance of the problems they suffer from, and is a cop-out. And just because some of us are privileged enough to be able to forget that history and therefore have the privilege of using these words while forgetting the context from which they arose, not everyone is that lucky, and it's basic human decency to be willing to be at least somewhat sensitive of that.
lolz
