I agree, both male privilege and female privilege are real and very serious problems. The existence of one doesn't negate the other. They are often interlinked, such as the male privilege of not getting lower pay and fewer career opportunities just because you have a child and the female privilege of being allowed to take more time away from work to raise that child and not being treated as a secondary parent. You can't solve one without solving the other.

The things you mention are not necessarily in that category, but seem to be because people are taught not to care about men as much. The flip-side could be our society's infantilization of women, but the harms of that are more subtle than the result of our society's indifference towards men, such as men receiving higher sentences for the same crimes and being refused help in situations where help is offered to women. Perhaps having fewer people encouraging women to take risks and fewer people being willing to invest in women is one of those harms.

I think the point is less about whether each type of privilege is real, but that this logic is incredible shaky. (i.e. deciding there is a bias against a group solely based on representation in outcomes)

Put another way (and I think the OP tried) if we look at prison sentences by gender and apply the same logic, then we have a huge bias against men in the justice system, yet no one seems to be making that case nor would it gain popularity.

Of course there is a huge bias against men in the justice system. That should be obvious to anyone, and is also confirmed by many studies. For example, from the US federal system:

> It finds large gender gaps favoring women throughout the sentence length distribution (averaging over 60%), conditional on arrest offense, criminal history, and other pre-charge observables. Female arrestees are also significantly likelier to avoid charges and convictions entirely, and twice as likely to avoid incarceration if convicted.

https://repository.law.umich.edu/cgi/viewcontent.cgi?article...

And the UK:

> We find significantly harsher sentences imposed on male offenders even after controlling for most case characteristics, including mitigating factors such as ‘caring responsibilities’. Specifically, the odds ratios of receiving a custodial sentence for offences of assault, burglary and drugs committed by a man as opposed to a woman are 2.84, 1.89 and 2.72

https://eprints.whiterose.ac.uk/154388/

Also see this article regarding the huge gap between the prevalence of sexual violence perpetrated by women against men and the prosecution of those crimes: https://malesurvivorbop.nz/wp-content/uploads/2019/09/Stempl...

The sorts of men who are thrown into cages are different sorts of men than those who are handed enormous sums of capital.

In some cases (see: SBF) they shouldn’t be.

neither category should be inhabited, so yeah.