Upon reading the headline I immediately wondered if childcare and cleaning were in the set of the female dominated careers.
My hypothesis is that men are considered much much riskier hires for certain roles.
The reason I thought of these two roles in particular is because socially I've often heard expressed worries that men in daycare are more likely to be sex offenders, and for cleaning I've often come across the sentiment that men are more likely to steal (in Sweden). If those beliefs are pervasive the discrimination should be reflected in the data too, as employers steer away from hiring men.
Indeed the discrimination effect is significantly weaker if you look at table 1 in the 'Data' section of study while discounting these two roles.