Possibility 2: Those fields are male-dominated because they can't get into female-dominated fields.
Men do not work as teachers because the media has painted men as "sex crazed". Most mothers would be uncomfortable with having a male 4th grade teacher for their daughter.
Many women would be uncomfortable having a male gynecologist or a male nurse helping them deliver their baby.
> Doctors (high prestige, high pay) are about 70% male.
Sorry but this breaks your narrative: 60% of new MDs each year are female. However: female MDs are more likely to quit the profession or go part time in order to raise kids. Again, this might show anti-male discrimination because it is not socially acceptable for male doctors to quit work to stay home with the kids.
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The above suggests to me that there's indeed a huge level of bias and discrimination, but not in the way you think.