El Macho
I've never seen it.
I saw more fights growing up in Boonton, NJ than in Mexico. I heard domineering, sexist remarks from my SIlicon Valley colleagues that I doubt any self-respecting Mexican would make.
I think the notion of the macho Mexican comes from travelers' cursory first impressions, based on observations of a sort of cultural playacting. The romantic image of the bullfighter laughing in the face of death is one.
Bullfighters don't want to get hurt. Like professional wrestlers, they know how to create the appearance of danger and injury, but they're not about to jeopardize their careers through disability if they can help it.

A bullfighter puts his masculinity on the line.
Mexican men are courtly and polite, generous and romantic. They comport themselves with transparent pride. They are shown respect by their women. But they do not necessarily wear the pants in the family.
Young couples who can't afford their own homes (and there are many such) often live with the wife's mother. Young husbands wind up being answerable to their mothers- and fathers-in-law. I know guys in this situation: there's nothing macho about them. Some of them actually whine. Girly men.
The women I saw in the villages of the Yucatan, Campeche, the Huasteca, submitted to no one. Many were heads of their households, the family decision-makers, ellas que cortan el bacalao (she who cuts the cod).
There's a childlike pretense about the swagger of Mexican men—of those who try to look macho, anyway.

Struttin' for the ladies.
They don't quite seem to bring it off.
At first glance, you see a lot of hyper-masculinity. Men appear to be fully in charge. But it's all just bad acting, wishful thinking, a fantasy.