I don't think the stigmatisation of men showing emotions is exclusively Anglophone culture. I live in Ireland and there isn't really a stigma of men showing emotions because of public awareness campaign about mental health for both men and women. But like you said, I've met couple of overly manly men jerks and uncaring women, but they're the ones not worth your time and in tiny minority.

In any case, some cultures have antiquated machismo mindset which is sporadic across the world.