If you are interested in MRA topics (especially if you're interested in arguments on things like disposability, threat narratives, and positive identities), I'd recommend a trip over to YouTube and checking out a couple of channels. GirlWritesWhat is usually the most popular one to suggest, but I'd suggest Alison Tieman who I think does a much better job at presentation. Honey Badger Radio is a podcast on those sorts of things, and they even covered the whole Zoe Quinn mess.
ContraryOpinions said:
The subject that first got me thinking about it was "male desposability", that is the idea the society deems males to be more disposable. Touted as an example of this is the life boat situation in which the order of places is assumed to be children then women and only last of all men. I found this interesting because, as a man I would (I like to think) follow that ordering. And yet strictly speaking this is a sexist attitude.
It's the classic example, but not the most likely example in a modern context (which is the most common argument against it, because they argue against the example rather than the concept).
Another classic example is Selective Service. The thing about Selective Service that they always seem to miss is that, even if we assume that conscription being political suicide in a ripple from Vietnam carries forward indefinitely, and accordingly the risk of anyone ever for the rest of US history being drafted is infinitesimally small, we still require young men to sign a document for the specific purpose of giving the government the right to send them to die should it ever see fit in order to receive the same legal rights and benefits that women are provided with no strings attached. Selective Service is literally "because you are a man, you have to agree that your life is forfeit if we want it (even though we probably won't) if you want the same rights and benefits as a woman."
More realistically, how about an experiment. Watch the network news for a few nights or check your local paper/local paper's website. Note how and when explicitly gendered words are used. Note the trend not to specify female-ness of perpetrators or male-ness of victims, unless they are actually named. Male perpetrators and female victims are more readily identified as such. Bad things are seen as worse when they happen to women, and bad things aren't seen as being as bad when they're done by women (and this shows valuing the lives of women over those of men). There was a study done wherein a survey was sent to a sample of psychologists that asked if specific behaviors were considered abusive, with male-on-female and female-on-male versions sent at different times -- every behavior was considered abusive by a larger percentage of completed surveys when it was a male perpetrator and a female victim than vice versa.
This is related to agency and how we perceive it -- namely that we will assign men agency in excess of what they actually have, and women agency beneath what they actually have. Which is why, for example, if a drunk man and a drunk woman have sex then it can be argued that he raped her, because her being drunk means she couldn't consent (intoxication robs her of all agency, minimizing her agency) but his being drunk doesn't remove his responsibility (his being drunk doesn't change his agency, to maximize his potential agency).
Another example regarding social perception -- there's a blog out there that exists for shaming men for sitting with their legs too far apart on public transit ("too far" seemingly meaning shoulder width or wider), deeming it a patriarchal display of dominance by taking up excessive space, or something to that effect. A woman sitting with bags in adjacent seats on both sides, to keep anyone from sitting beside her without her first being able to filter them? Suddenly that "taking up space" thing isn't some kind of dominance display and is instead OK, even reasonable.
Another unrelated situation is when women enter into male-dominant spaces and when men enter into female-dominant spaces. In the former case, we expect men to change the space to prevent the woman from being uncomfortable, in the latter we expect the man to change to prevent the women from being uncomfortable.
To hook into the whole Quinnspiracy thing, people have said that it wouldn't be this big if Zoe were a guy. Personally, if we gender flipped that whole mess, I expect we'd have had news articles about how Male!Zoe was a rapist and abusive and how Female!Eron was brave for coming forward about what they'd endured posted on the day thezoepost went up. After all, "a friend of a friend said you raped her" was enough to get people demanding we boycott Cards Against Humanity.
ContraryOpinions said:
Another example that came to mind was reproductive rights. In this we have a undeniable biological difference between the sexes (indeed THE difference). In the name of an egalitarian society, BOTH parent should have equal rights over any children (even unborn). Yet this clearly isn't, and possibly cannot be, the case. If, for example, the mother wants an abortion and the father wants the foetus kept the deciding vote is (rightly) the mothers.
There's a deep well of things related to reproductive rights and father's rights that could be gotten at.
For example, it's a common MRA position to push for a rebuttable presumption of shared custody -- that is, that family courts be required to start from the position that both parents have an equal right to custody, which must be challenged to move from that position. One of the largest feminist lobby groups in the US (the National Organization for Women) has consistently fought against that.
Another common MRA position regarding reproductive rights is that, since they can't be equal due to biology, they should be as equitable as possible. This usually involves arguing for an option for nullifying all parental rights and responsibilities (everything, essentially a legal "is not the father") under a limited time range (usually one shorter than the limit for abortion to allow the mother to take it into account when considering abortion) or a fixed number of days after being made aware of paternity (specifically to prevent his being denied the option by being kept ignorant of pregnancy until it's too late). This is usually argued under the position that women have the right to terminate all rights and responsibilities of parenthood through abortion, adoption, or "safe harbor" abandonment without the father's knowledge or consent and accordingly something similar should be available to men. Some proposals go so far as to argue that the man being equally responsible for the pregnancy occurring also holds a responsibility to share in the burden of the pregnancy however it is resolved, and accordingly should be required to shoulder a share of the woman's expenses in dealing with the pregnancy however she chooses, but this is less common to even bring up.