In the sense of paternity, which is focusing on the purity of the Israelite line, only women are barren, only women are infertile. Males are always fertile even after death. But in the depiction of the story of Abraham, you have, first of all—before you get to Abraham—you have this construction that says men beget men; you don’t see women anywhere in their genealogies.
But when you get to the point where you’re going to talk about Abraham, you suddenly see Sarah being introduced, but the focus on her is that she is barren. And then, the promise is made to Abraham that he will have many descendants. He realizes that there is a famine and he has to go to Egypt; and when he’s in Egypt with his wife, he says, “You say you are my sister” and she is taken into Pharaoh’s household, so that you would have questions of whether the descendants of Abraham are really Abraham’s children.
But Sarah is barren so there is no pregnancy that is going to take place and also, God will have closed off the wombs of Egyptian women. So, the Egyptian Pharaoh is not infertile, he’s not incapable of impregnating Sarah, but it’s God who intervenes and shuts off the women of his land.
When we jump over to where it has been identified that Sarah is really going to be the mother of the favored child, Isaac, it’s mentioned in chapter 18 (chapter 17 and 18) but in chapter 20 Sarah again is taken by the Philistines, I think; and in there, now we know she is not barren but it’s made such that she is not taken into the house of the Philistine king. In a dream it’s revealed to him that actually Sarah is not Abraham’s sister but his wife. So the possibility [exists] that when Isaac is born in chapter 21, that they would have those questions of “Is this really Abraham’s child or a Philistine’s?”
The reference to how Sarah becomes pregnant does not make it as if she had sex with Abraham. It makes it like Yahweh visited her and, but there’s no sex that’s mentioned directly—that Yahweh remembered and came to fulfill Yahweh’s promise that she would have a child and she does, she conceives—as if this is taking place between God and Sarah and Abraham is not involved. But when you move to Hagar, it’s made graphic. Abraham has sex with her, he went into her and so you see [it] graphically but she is rejected, she’s not the child of promise; so you have the sex that’s valued, that’s being promoted is the one that is focused on the purity of the Israelite line.