That's not me saying those things or deciding they are the rules for the Man Box. Those are the things that guys say about what is expected of them, as per many, many research studies. Naturally, not every single guy buys into those at the same level or at all, and younger men resist this more than older guys but it is what research of this topic reveals - from a variety of studies. The man who wrote that story is an expert in this field, a scholar who has studied this topic for decades. He's not some guy getting feelings off his chest.
First you say that men are vulnerable and now you say that it doesn't benefit them. Yeah, because of Man Box culture - and it's isolating, something that humans are not naturally equipped for, so it drives suicide. Again, this is very well documented. In prior decades people spent less time indoors on the internet and more time in social gatherings, including organized religion - which has it's downsides, but at least provided community for men. You are correct that Man Box patriarchal culture (which women uphold to some extent as well) still makes it difficult for men to truly be vulnerable - but that's a different problem than what you initially said, which is that they already are. Everyone should only be vulnerable around people they can trust. That's not exactly a news flash, but it's still not a quality that is widely valued in Man Box (patriarchal) culture and that hurts boys and men.
Feminism has nothing to do with it - if you (a person, not you in particular) are so pathetic that people who have long been marginalized and discriminated against finally getting a small bit (far from total) equality knocks you off the rails, then you have a lot of problems that have nothing to do with women's opportunities or equality.
I do genuinely care about men, and the state of our culture. And, my husband comes home and tells me all the time about how hard his week has been. Sometimes he cries, because his boss is a total asshole. I value that, even though I hate that we live in a culture where a boss who acts like that reads as a leader, and I don't think any less of a man who cries. Some women do, but again, that's due to internalized patriarchy - a social system that needs to go so that people can just be whomever they are without others getting in their face and telling them they ought to be different.
If you've never heard of Brené Brown, check her out. She's got a Netflix special as well as a ton of books, articles, etc. She's the world leading researcher on vulnerability and shame, and she's a Texan who is funny as all get out. She also works with a lot of Silicon Valley execs, law enforcement, and the Air Force Academy. Her work is real, honest, non-judgmental, and important AF for our culture to move into a better place. Here's a link to her first TEDtalk on vulnerability which is one of the most watch TEDs ever.
