(This was suppose to be post 2 below the other but whatever) In your society a female birth is cheered a male birth is met with solemn gazes (actually somethin that happens in the inverse today aka male is celebrated)
To think on: Culturally How will death work in this world? Will the male be burned alive or entombed with the body of his wife once she passes? Cuz women had to do that.
What is the story told to all in the same vein as adam and eve for your world? What did the man screw up so badly that all men are the way they are today? And if the modern man is not that way he should strive to be it only producing a child should be the end all be all to his happiness and of course making sure that child is a functioning adult but also his home is shining example of what it is to be orderly (if one values this for the culture at all) ect.
Did some king forever ago screw up so badly and his male cabinet along with him it was beyond hand waving it away? Did they fall in death, disease, and famine so badly due to these men that it was either given or (more likely) wrestled from the broken man's hands and his wife took power over him as he'd done too much damage and too much shame towards their people and herself she could no longer suffer his disasters to go on? The very earth itself lashed back at man and slowed his production of males from his seed with every plant he ate and each drop of water that rained upon him or he cupped from the stream so more and more women were born to one male as to choke such evil and want for causing others to suffer for him out of the world leaving women to take up the mantel in full and in higher and higher numbers.
His crusading wife in turn raised up the women and they proceeded to crush them in a burtal fashion maybe this first retaking wasn't done in frontal assult but cunning or gruella warfare with a later routing battle maybe plunging the men into a gorge in a symbolic way she and her women cast these invading men who crushed, broke, and humiliated her husband into the literal earth that now kicked back at the male in time with her displayed bloodrage. She avenged her own shame but her suffering had only begun as she transformed into spear point she would not nurture what she bore she was now a weapon.
Women still war but the death rate is less or if it's not then the victories and defeats more spectacular due to tactics being ever more fluid and well researched, women can be however more rutheless, more bloody, and more torturous in their responses when pushed. In your case is this still a thing or is such extremes punished to satisfy the earth of her ill behavior?
Does your society cave out a rare space for a male on the battlefield or in church? Is he a war witch designed via rites and rituals to give strength to his women? And it would be his women in a careing manner not his women in a possessive manner he loves his women in a paternal sense his rituals it is thought to dispense more strength and possibly imbued the women with heart of concern for their own men left behind to induce them to be more rational or more swift whatever you'd like what do they value most? She is suppose to go to war because she shows she cares via shedding blood of those who would harm her family she is his teacher to show her faith to god she tutors him to patience, think of others, selfless, (whatever culturally they think he needs), and she shepherds him. He shows his repentance by submitting and perhapse ritual he shows he cares for these lessons by caring for the children and tending the home and him being the full cultural plus package it shows to the cosmos he truly wishes to amend the wrongs adam did to the earth and possibly god.