I think one of Shakespeare's works speaks eloquently to his lack of misogyny. I give you Kate's ending soliloquy in "The Taming of the Shrew."

You would have to be half dead not to notice how wonderfully ironic this soliloquy is. The shrew, the harridan, the woman who cannot be tamed, suddenly throws off her entire personality and embraces Woman's Submission to Man. The play is a comedy, and her speech is funny as hell; she mocks the submissive by pretending to and exaggerating it.

Very likely, Shakespeare was cleverly avoiding condemnation by the ruling class. I do not think the working class was terribly hung up on women being submissive in his day, but the nobility was another matter - and they could swat down a struggling playwrite with a whim. So he gave them Kate - who on the one hand proves just how brilliant a feminine speaker can be, but then in the end she conforms... really conforms. Conforms so absurdly, it's hilarious. Nobles could not complain that the play violated their sense of propriety. But she did violate it, and it was a joke the audience got. Irony heaped on irony.

Homer was good. But nobody did irony like Shakespeare.