I participated in men's work, not specifically the ManKind Project but a closely related organization. I personally found it helpful doing weekly check-ins and having people holding me accountable to my goals. Unfortunately, the stigma regarding men sharing feelings is prevalent in western society, and it's not only the men causing it. When I told several female friends about the work they did, their response was: "A…
Our society will always value men who are confident, this is so much deeper to me than being scared to share your feelings because “it’s gay”. Women are attracted to confidence, employers reward confidence, hiring managers are impressed by confidence. Vulnerability and weakness are just not rewarded for men or women, but especially for men.
https://www.youtube.com/watch?v=btud-zsdmk4
There are definitely caveats to this. It has to be done a certain way. It works better when you already have some status. And I'd absolutely agree that society lets women express more vulnerability than men. In a hypermasculine environment like a group of socially clueless 20something males at a tech company, you will probably want to show vulnerability less often.
But with the general population and normal people, it's really fine and even good to show some vulnerability, just do it in the right context.