In his masculinities and crime, what did messerschmidt call men's struggle to dominate women in order to prove their manliness?

It is called "doing gender".

The book is testing the regular masculinist character of criminological research, James W. Messerschmidt builds up an intricate investigation of the gender orientation roles that, alongside class and race, impact the event and kinds of violations in our general environment. It contends that his utilization of the focal term `masculinities' is redundant and that the contentions connecting manliness to wrongdoing are far fetched and coherently defective.

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