Sarah, Rebecca, and Rachel all went through seasons of barrenness before they bore children, even though each was promised a great nation through her womb. The sages asked why the Holy One, who could have opened their wombs at any moment, left them waiting so long.
They offered three answers, and each teaches a different lesson.
First, the long wait kept the matriarchs from relying on their own merit. None of them could point to her righteousness as the reason she had children. Each had to admit, in the moment of finally conceiving, that the gift was not earned. Barrenness is a fence against pride. A woman who has waited decades for a child does not hand that child around like a trophy she won. She hands him around like a miracle she received.
Second, the long wait pulled them out of the orbit of idolatry. Many of them, as young women, had lived in homes where their parents served idols. Some had briefly been delivered into the hands of idolatrous priests, as the tradition reports of Sarah in Egypt and of Rachel in Laban's house. Had children come easily, the young mothers might still have wondered, in a corner of their minds, whether the blessing had been arranged by the old household gods. The long wait made it impossible to credit anyone but the Holy One. Idols do not wait patiently for a decade and then deliver.
Third, the long wait taught them to pray. The matriarchs became master petitioners. Rachel said to Jacob, "Give me children, or I die" (Genesis 30:1). Hannah, later, in the mold of the matriarchs, would pour out her soul before the Lord at Shiloh (1 Samuel 1:15). The prayer of a woman who cannot stop asking is one of the most powerful instruments in Jewish theology, and the matriarchs are the ones who forged it (Gaster, Exempla No. 287).
The sages concluded that the long barrenness was not a cruelty. It was a schooling, and the lessons became the three pillars every descendant of those matriarchs would stand on.