Virgin Knight who is the Frontier Lord in the Gender Switched World - Chapter 1

That world would never occur like that. Ever.

Here is why:
Reason 1:
Let’s say you’re in a world where, for reasons, women outnumber men 10,000:1. Male gametes are determining the gender. In such a world genes of a men whos gametes are skewed towards more males would be exceptional well. Genes of women whos gametes are skewed towards selecting male offspring also would do exceptionally well.
Because of higher reproduction rate a lot more males would be born, until the ratio is 1:1.
If there are more males than females the selection pressure go the other way round until there are around 50% of each gender.

Reason 2:
To produce offspring a men has to invest, outside of mating rituals, only about 30 minutes to an hour of physical activity and the energy for gametes, that amount for less than that.
A woman, however, has to spend ~10 months in a vulnerable state, has to spend enough energy to grow another human being, has to go through a very dangerous birth (not uncommon for the woman to die, or the mother and the child), and spend even more time and energy to raise (breastfeeding , among other things) the vulnerable offspring to a state where it isn’t dependent on the mother anymore.
That is why women will never behave like men, and always will protect their chastity/select their partners carefully.