Demetrius. She is a woman, therefore may be woo'd;
She is a woman, therefore may be won;
She is Lavinia, therefore must be loved.
(Titus Andronicus, 2.1.636-638)
Titus Andronicus, bloody and horrifying, is a hard play to watch. Although we can read it as Shakespeare's "slasher film," I think that we can also look at it as an exploration of excess and the consequences of taking ideas - beliefs, cultural values - to their logical conclusion or end point.
Take the treatment of women in the play, for example. Obviously the final fate of Lavinia - raped by the killers of her husband, her tongue cut out, her hands chopped off, ultimately stabbed to death by her father - is not something that most people would think is okay. It's violently excessive, right? BUT - and I think this is the important part - Shakespeare shows us the kind of attitudes toward women that can lead to this kind of result.
Demetrius and Chiron don't start out plotting to rape Lavinia - they just think she's cute and want to seduce her away from her husband. They say that they "love" her. But we've seen this sort of slippery slope before in The Two Gentlemen of Verona - would-be rapist Proteus starts out by trying to actually win Silvia's love, but when she won't agree, he decides he's entitled to take what he wants. Interestingly, both scenes where the women are threatened with rape take place in the forest, away from the structures and safety of civilization - Silvia is saved seemingly by a miracle, but in Titus, where everything goes to the logical extreme of the idea, there are no miracles to be had.
I think that the question being raised here, in both plays, boils down to this: what are women actually for? (This isn't a joke, by the way.) We've got Demetrius' answer, quoted above: She is a woman, therefore may be woo'd;/She is a woman, therefore may be won. But Demetrius, a pagan character from the classical past, isn't the only Shakespeare character who says this - Suffolk, an English nobleman in Henry VI Part 1, says almost exactly the same thing, word for word, about the woman who later becomes the queen of England! She's beautiful, and therefore to be woo'd;/ She is a woman, therefore to be won. Brings it a little closer to home, perhaps?
In both cases, these sentiments seem to just go by without much discussion or comment. Perhaps, watching the play, one might feel either mild disagreement - or agreement! - with this answer to the question what are women for. But then Shakespeare shows us Lavina, and we have to face the logical end result of a belief that women exist to be wooed and won by men. We see Lavinia - brutalized, tramautized, humiliated, alone in the forest spitting out blood - and the play seems to say, Look! How do you like this now?