In many ways, Christine de Pizan credits the writing of The Book of the City of Ladies to an obscure writer named Mathéolus. If this dude hadn't written a book about how horrible women were, Christine might have never found it necessary to respond to his arguments. As she writes at the beginning of her book,
I started to read [Mathéolus' book] and went on for a little while. Because the subject seemed to me not very pleasant for people who do not enjoy lies, and of no use in developing virtue or manners, given its lack of integrity in diction and theme. (1.1.1)
Basically, she criticizes the book for being dumb and poorly written. But she does realize that there are many better writers who have also said horrible things about women, and this is what causes her to think more about the issue.
As The Book of the City of Ladies unfolds, Christine de Pizan becomes more and more convinced that writers like Mathéolus should stop writing such lame books. As she writes at one point,
Let Mathéolus and all the other prattlers who have spoken against women with such envy and falsehood go to sleep and stay quiet. (2.19.1)
This is probably the most direct insult she makes to any man in this entire book. But what's really ironic is that nobody today would remember Mathéolus if he weren't mentioned in Christine's book. The Book of the City of Ladies is famous today and only a handful of people have ever bothered to look at Mathéolus' work. So this guy only really exists today as an antagonist who Christine might as well have made up.
And that is sweet Justice, with good Reason, for Mathéolus' lack of Rectitude.