Why didn't Avraham tell Sarah about Hashem's promise to have Yitzchak?

Question

At the end of Lech Lecha, Hashem promises Avraham that Sarah will give birth to Yitzchak, which is followed by Avraham performing a bris on his entire household including himself. Three days later, Avraham invites the angelic caravan into his tent where they restate the promise of Yitzchak, leading Sarah to laugh as she was never informed of this prophecy.

Although Avraham may have been busy and in pain from the bris, Avraham seemed to have enough strength to run after the caravan. Why didn't he tell Sarah about the eventual gift of Yitzchak?

Answer 1

The Ramban Bereishis (18:15) suggests two potential answers, though only proposes both as "maybes":

ברהם לא גילה לה הנאמר לו מתחילה (בראשית י״ז:י״ט) אבל שרה אשתך יולדת לך בן אולי המתין עד שלוח השם אליה הבשורה ביום מחר כי ידע כי לא יעשה ה' אלהים דבר כי אם גלה סודו אל עבדיו הנביאים (עמוס ג ז) או מרוב זריזותו במצות היה טרוד במילתו ומילת עם רב אשר בביתו ואחר כן בחולשתו ישב לו פתח האהל והמלאכים באו טרם שהגיד לה דבר - It is proper that we also say that Abraham had not revealed to her what had originally been told to him: Indeed, Sarah, thy wife shall bear thee a son. Perhaps he waited until G-d would send her the announcement on the following day for he knew that the Eternal G-d will do nothing, but He revealed His counsel unto His servants the prophets. It may be that due to his great diligence in fulfilling commandments, he was occupied with his circumcision and the circumcision of the many people in his house. Afterward, on account of his weakness, he sat at the doorway of the tent, and the angels came before he had told her anything.

(Perhaps Sarah/the women of their household did not enter Avraham's tent for modesty purposes as the men were recovering from a sensitive surgical procedure? If that is true, Avraham may have planned to tell Sarah in person after he recovered.)

Answer 2

We don't see any reason to think he didn't tell Sarah. So why did Sarah laugh? Sarah was a tzaddika, and a prophet greater than Avraham, let's give her the credit she deserves.

She heard the bracha/prophecy, and she laughed because she heard something wrong with it. It sounded like it was temporary, so she laughed as if to say "you call that a bracha?". The malach respondes הֲיִפָּלֵ֥א מֵיְהֹוָ֖ה דָּבָ֑ר and reassures her, so her laughing was lobbying for her son. The malach said אָשׁ֥וּב אֵלֶ֛יךָ כָּעֵ֥ת חַיָּ֖ה וּלְשָׂרָ֥ה בֵֽן, which is actually a reference to after the akeida: same malach who told Avraham to put the knife down was the same one now giving the bracha! When Sarah got the news, our imma Sarah was able to die reassured that she had saved her son, by laughing and insisting on a complete bracha.

She, as with the Shunamit woman, were not saying "I don't believe you" through the laugh, they were both saying "I don't want something temporary". Avraham didn't pick up on it, because he was a seer prophet ("he raised his eyes and he saw"), Sarah was a hearer ("Sarah heard"). What did she hear? A bracha, to be permanent, must be face to face, and she spotted that the malach gave her the bracha, but to Avraham! וְהִנֵּה־בֵ֖ן לְשָׂרָ֣ה אִשְׁתֶּ֑ךָ Something sounded fishy about that...

https://www.youtube.com/watch?v=Q6Qgz1o7cgM&ab_channel=RabbiYoniKatz