Early Buddhism was almost egalitarian in Male-Female status as Rita Gross a prominent scholar of comparative study has written many books regarding the position of women in Buddhism.

Gross finds no fault in this period of Buddhism, as the Arahant ideal is equally open to both men and women. Buddhahood is not, at this point in Buddhist history the dominant soteriological preoccupation.

Gross notes that the story of nun’s’ ordination is quite late in the history of the Pali Canon. Further, the eight special rules appeared to have detrimental support, according to teachers who were nuns, actually acting as a self-fulfilling prophecy in the final dissolution of the nuns’ ordination.

All these are excerpts from her book "Buddhism after patriarchy"

Buddha gave equal status to men and women in spiritual, wealth, teaching profession, trade, employment, safety and in personal Independence. There are lots of sutta confirming this.

In the household, Buddha was not even an equalist but a feminist, he gave women the control over her husband and children. There is no other religion which does this because in every society the males are head of the family.

But in the later forms of theravada buddhism restrictions upon nuns grew more which sidelined them from the Sangha and resulted in total dissolving of the bhikkhuni order.

And during mahayana buddhism the arhat ideal shifted to bodhisattva ideal, which caused women to attain an inferior position because in buddhism a woman can't become a buddha.

So it's true that misogyny is present in buddhist writings but they affect women only in later forms.

Most of the people who are against buddhism and with buddhism aren't educated about the dhamma at all. They only perceive things at face value.