We can well understand Sarah’s sadness in not bearing children. She had a maidservant, Hagar, who was her maidservant. Hagar is referred to later in the chapter as שפחת שרי.
Sarah said to Avraham, “Until now we haven’t had children. Although you deny it, I know that the fault lies with me. (Sarah’s words indicated this when she said God עצרני has held me back from giving birth.)
She asked that Avraham marry Hagar fully as his wife. At the same time, she wanted her relationship with Hagar to remain the same. Hagar would remain dependent on Sarah.
Sarah had intended to raise the child from that marriage as her own. “Perhaps I will be built up through her.” (As RSRH explains: There is a concept of a house in the dimension of time. All of history is ongoing work on one great building. Each generation is a building block in that great edifice. This is the meaning of the blessing that is said at a wedding: והתקין לו ממנו בנין עדי עד – God created man in His Own image. From man He has established Himself a building reaching into eternity.)
Avraham agreed to this, not for his own sake. He believed he would yet have children from Sarah. He did this to fulfill her personal wish. (And Sarah requested this not for her own sake but for Avraham’s sake. She had told him, If you won’t do it for your sake, then do it for my sake!” – to convince him to agree.
Beraishis 16: 1-3
pages 368-370