When feminists bring up "male privilege", it has often caused me to think of the many ways that females are privileged. These things are often not complained about by men, and there is no political ideology for men that capitalises on their sense of victimhood, as there is for women.
Female privileges:

• Lower sentencing for the same crime
• Drastically better outcomes in family courts than men
• Not drafted to war
• Negative statements about individual women or women in general are 'misogyny'. Negative statements about individual men or men in general are socially acceptable and even celebrated.
• Women benefit from the status of being automatically seen as the underdog and the victim. They therefore get preferential treatment, affirmative action, and the benefit of the doubt.

But most of all, females have MASSIVE privilege in terms of sex. This is where feminists want to have their cake, and eat it too. They want to vilify men and masculinity for certain things, without wanting to give up the power that is the root cause of those things. Not that they could give it up anyway, as this state of affairs is biologically hard-wired, and not merely a social construct.

You know the 'key and lock' analogy? "A key that can open any lock is a great key (stud), but a lock that can be opened by every key is a terrible lock (slut)."
As comedian Jim Jefferies puts it: "When you have a baby boy, as a father you think 'I hope he bangs all of the girls in the neighbourhood when he grows up. But when you have a baby girl, you don't think 'I hope she bangs all of the boys'. In order to sleep with a lot of girls, a guy needs to be some combination of good looking, funny, and wealthy. In order for a girl to sleep with a lot of guys, she just needs to be there."
Now, this might seem like a sexist double-standard. But it underlies a deeper truth about reality: women are more valuable than men. They can give birth and create life. Men are disposable, and have always been treated as disposable throughout history. Men hold women up on a pedestal; part of the dynamic of men being the hunter and women being the hunted, is that in being the hunted they are also the prize. Women use and abuse this sexual leverage every day without even realising it. Yet, they can't really be blamed for it, because that's just the way that nature is. If you don't think that women have power over men, that just reflects the fact that you are blind to your own privilege. Even if society could drop these 'standards', which you say are so harmful, women wouldn't want to, because they benefit far too much from the fact that men essentially worship them.
Your article, and feminism in general, tries to deny reality by incorrectly claiming that gender is a social construct and has no inherent foundation to it. More than that, feminism is downright hostile to masculinity (and also femininity), to the point of wanting to erase them entirely, and wanting to live in an androgynous dystopia.

I would also challenge you to show me where exactly institutional male privilege exists, given that the wage gap myth has been debunked about a million times, and no serious economist accepts it.