I'll address their arguments in two parts: firstly the substantive parts, and then the strawman dictionary argument.
But this is really beside the point. And that is, OR-sexism collapses the entire system of kyriarchy down to a single oversimplified notion: That all men always have the social leverage to enforce or exploit their prejudices, and that no women ever do. But this is simply not the case. In the kyriarchy, different groups experience power advantages in different ways, in different contexts, and at different times. There is no one Group With All The Power, and no Ultimately Victimized Group. It doesn’t work that way, and frankly, the Oppression Olympics hurt everyone and help no one.
Firstly, they clearly mistake my argument. Simply put, what we call "sexism" is a term that is used to describe the manifestations of a large system that privileges men (and certain types of men). While I certainly agree that men can be discriminated against on the basis of their gender, that's not sexism the same way the above-mentioned sexism is sexism.
And this is an important point: the discrimination against women and discrimination against men are not the same types of discrimination. Their overall cause, our cultural system, is the same, but their manifestations are starkly different, bringing the issues to light is very different, and solving the issues is different. I think it's very important within feminist circles to be very clear in the terms we use, because using the same language to describe problems that have very different approaches to solving them is confusing.
I've talked a lot about how I believe a "problem" of feminism is that it is extremely ineffective at reaching "mainstream men." As in, your white, middle class, cisgendered men. Feminism casts issues from a feminine perspective, generally, because by using shared and common experiences, you can best reach your target audience. As a male feminist, attempting to reach a male audience, I (and people in our movement) need to use our shared and common experiences, which are necessarily different in many respects than women's experiences, in order to reach men. This necessitates a fundamentally different approach.
As I said within the context of talking to men about sexual assault: "talking to an oppressor is different than talking to the oppressed." That's not to say that men are not victims of the system we live in, and that many men do feel (rightly so) as if the system disadvantages them. Our system privileges certain men who perform masculinity a certain way. All "acceptable" masculinities have limitations, and men are no less victims to this than women are. However, they are not victims of the same things in the same way.
One of the reasons I sometimes cross-post, and I enjoy reading, Manboobz, is that David Futrelle's shining of a light on the MRAs also shines a light on a lot of underlying feelings and anger that men have at the system in which we live. While I tend to think that most of their ways to address or process their anger is misguided, it's there, and it's something we, as a feminists, have to find ways to address.
A second part of their argument, which I can't simply let slip by, is their reliance on the dictionary. Doctormindbeam writes, adding a dictionary definition at the end:
To begin, a linguistic pet peeve: words mean shit. You can’t simply redefine them to suit your needs. They have meanings, and they’re there for a reason. Namely, so that we can all fucking understand each other. In particular, “sexism:”
This is a pet peeve of mine. Dictionaries are great things. If you don't know what a word means, they can give you some pretty solid general definitions of words. But they're generally pretty poor at giving exact, specific, and academic meanings to words. Quite topical that this has happened this week, as this was brought up in the legal context by Adam Liptak, the Supreme Court Correspondent for the New York Times. He wrote in the context of Supreme Court Justices using dictionary definitions as evidence of the meaning of Constitutional phrases. Jesse Sheidlower, Editor at Large of the Oxford English Dictionary is quoted in the piece as saying: "I think that it’s probably wrong, in almost all situations, to use a dictionary in the courtroom[.] Dictionary definitions are written with a lot of things in mind, but rigorously circumscribing the exact meanings and connotations of terms is not usually one of them.”
This equally applies in an academic setting or in other settings where we ascribe very specific meanings that represent complex ideas and theories to single words. If we moved out of the realm of the feminism, for instance, and sought out a definition of "communism," I'd suspect we'd find as many definitions as we have dictionaries, and more than a few people who have been willing to fight and die over those definitions. Recourse to a dictionary is a strawman argument that obscures actual differences in ideas and theories.
I'd also note, for the record, that the definition used is from wikipedia, and it has a warning at the top: "The examples and perspective in this section may not represent a worldwide view of the subject. Please improve this article and discuss the issue on the talk page. (January 2011)"