To me it's obviously sexist. But is it misogynist?

The intent of the statement is not hateful, it expresses that women, many women, often need to be dealt with using more patience and understanding, with different expectations and standards than what you'd hold men to. To not to take them seriously too often, especially when a woman says something absurd or outrageous.

Because it's not hateful and based in reality, it's therefore not misogynistic.

Relevant Classic Article

And no, women aren't children, for those who want to sperg off about that.