My overarching theme:

Today's society is not male or female dominated, neither were the majority of past ones. It is almost always technology and biology that defines gender roles, not pure societal construct.
There is some sexism currently in the system, which sometimes acts in favor or men, sometimes in favor of women, but the big differences in payment, jobs, roles is primarily caused by biological differences, not sexism.
By and large, big changes in gender roles where caused by change in technology. These roles were not injustices, they simply made living more efficient.
People suffered since the dawn of civilization, but those societies who understood the diference between men and women suffered a bit less.

Part one: Men are screwed over just like women are.



Statement 1: more men die or become cripples in wars than females


Source1:

WW2 was such a bloody war that the national ratio of men vs women changed for many countries that participates.
WW2 is a good example for what a total war looks like.

https://www.ucis.pitt.edu/nceeer/2007_820-4g_Brainerd1.pdf

The Soviet Union suffered devastating population losses during World War II, currently
estimated at 27 million or nearly 14 percent of the prewar population. The disproportionate
deaths of young men resulted in a drastic change in sex ratios among the population surviving
the war. For example, the ratio of men to women in the 20-29 age group declined from .96 to .70
between 1941 and 1946.

Source2:

https://fas.org/sgp/crs/natsec/RL32492.pdf

The American war on terror is a good example on a modern, smaller proxy war. Obviously it is MUCH less bloody than WW1 or 2.

There are statistics for multiple wars/operations in this document, here is an example:



 Operation Enduring Freedom (OEF): Military Wounded in Action

 Gender
Female 383 314 6 29 34
Male 19,645 13,892 375 4,893 485
Not Specified 66 0 42 23 1
Total 20,094 14,206 423 4,945 520


Statement 2: Dangerous jobs tend to be primarily done by men, not women.

https://www.bls.gov/news.release/cfoi.t01.htm

Fatal occupational injuries counts and rates by selected demographic characteristics, 2016-17

Women                                               |     387  |     386  |    0.6   |    0.6   |    0.0   |    0.0
Men                                                 |   4,803  |   4,761  |    5.8   |    5.7   |    0.0   |    0.0





Part two: There are differences in personality between males and females and that is not due to society.



https://journals.sagepub.com/doi/abs/10.1111/j.1745-6924.2008.00096.x

In recent years it has been presented as a reason that there is little, if any, mean sex difference in general intelligence, yet males tend to be overrepresented at both the top and bottom ends of its overall, presumably normal, distribution.


https://www.ncbi.nlm.nih.gov/pubmed/19883140

Results showed that men prefer working with things and women prefer working with people

https://www.frontiersin.org/articles/10.3389/fpsyg.2011.00178/full

women reported higher Big Five Extraversion, Agreeableness, and Neuroticism scores than men.

https://psycnet.apa.org/record/2012-10804-001

Gender differences were found suggesting that women, on average, have higher levels of neuroticism, extraversion, and agreeableness, while men are more open to experience.


Men are stronger than women -> they can handle physical labor better

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4315909/

https://en.wikipedia.org/wiki/Marathon_world_record_progression#Men

https://en.wikipedia.org/wiki/List_of_Olympic_records_in_weightlifting

This is so obvious that I am hesitant to bring more proof.
Just look at the amount of testosterone an adolescent boy vs girl has, the hormonal change a woman goes through each month, and the change in strength these hormones give you.

Last, but not least:

https://en.wikipedia.org/wiki/Equality_of_outcome#Comparing_equalities:_outcome_vs._opportunity

As long as ANY kind of biological difference exists in the sexes, you can't have equality of outcome (like equal pay, equal representation in parlament, etc) without sacrificing equality of opportunity.
The more fair and egalatarian you are (with opportunities) the bigger the gap becomes simply because of math and logic