A common claim women make is that men need to relate to each other more, express their feelings, etc. and they blame machismo for men not being as that.

However, reality shows another picture.

If you go to the Middle East or even some Mediterranean countries, you observe how men often kiss each other and bond strongly, while their culture is still very homophobic and has machismo. Now, the later is not ideal, but clearly those cultural features do not prevent men for relating to each other... actually it may be the opposite, maybe what women label as machismo is just men relating to each other.

The problem in the West is that a lot of male only spaces has been made mix gendered or demonized. The archetypical example was this article from Rolling Stones magazine. From then on, a lot of fraternities and male only spaces has been demonized.

Now, only male only spaces in the West are gay spaces, which automatically makes heterosexual male only spaces associated with homosexuality. Most men are not gay, so they don't want to be associated with those spaces, same as heterosexual women do not want to have relationships with men they suspect are gay, which is reasonable.

TLDR: Machismo is not an obstacle for men to relate to each other, and actually probably some healthy "machismo" is needed for men to bond in the first place. The demonization of male only spaces in the West and the reassociation of them with gay spaces made heterosexual men heavily reliant on women to relate socially... which is probably what women wanted after all.