I think you are conflating men as a group with men as individuals.
I don't, but most feminists do.
I think when they say "men are the problem" that's shorthand for a system
Then they should blame society, not men as a group. Most men don't have any more influence on the system than most women do.
And what do you think constant negative messaging about men as a group being the problem does to the minds of boys growing up? Are you surprised many of them go down the alt-right radicalization pipeline?
a system that generally pays men more
I don't know where this is true, but certainly not in Western countries, where such discrimination by gender is illegal.
expects them to take on less domestic responsibilities
More a question of expecting men to take on different domestic responsibilities, on top of expecting men to be the primary providers.
allows them to vote away women's rights
Instead, men overwhelmingly voted for granting women equal rights.
and all of the other longstanding injustices
You mean injustices such as conscription, age of retirement, homelessness, etc?