There are famous questions in the beginning of this week's Perashah, Perashat VaYera, regarding Sarah Immenu's laughter upon hearing that she would become pregnant and give birth to a baby boy.
1) We know that she was righteous and had faith in Hashem, so why did she laugh?
2) Why did she deny it afterwards?
3) How come she was rebuked by Hashem for her laughter, but in last week's Perashah Abraham also laughed when he heard that they were going to have a baby boy like the verse said:
ויפל אברהם על פניו ויצחק And Abraham fell on his face and laughed
And not only was Abraham not rebuked for laughing, but Hashem responded by commanding Abraham to name his son Yiss-haq, which means 'he will laugh'. This shows that Abraham's laughter was not just overlooked, but it was so good that Hashem highlighted Abraham's reaction by instructing Abraham to actually name his son Yiss-haq.
Ramban explained that Sarah did not realize that these men were angels delivering a message from Hashem. She thought that they were ordinary men. Similarly the Abarbanel explained that she thought that since they ate at their house, they were just giving their blessing to Abraham and Sarah, like guests often do out of gratitude for their host's hospitality. Ramban also suggested that it's possible that Sarah didn't realize that they were angels because she didn't actually see them. The verse reported earlier that they asked Abraham, where is your wife Sarah? And Abraham answered, she is in the tent.
Regarding Sarah's laughter the verse reported, ותצחק שרה בקרבה And Sarah laughed to herself
The Radaq explained that she didn't laugh visibly out of modesty. But the Ramban explained that laughing to oneself is a laughter of mockery, as opposed to visibly laughing with your mouth, which is laughter of happiness. Abraham's laughter was good because it was happy laughter. Sarah's laughter wasn't good because it was out of mockery. Ramban wrote that she should have had faith that it was at least possible and answered, Amen, may it be His will.
The Ramban also explained that Sarah didn't know that Abraham prophetically knew that she laughed. She thought that he detected it from her facial expression. So she denied it because she became afraid when she saw that he was upset about it. She believed that most probably Abraham was upset because she didn't react to the news with happiness and praise to Hashem. But then when he insisted that she did laugh, she realized that he knew about her laughter prophetically. The Ramban went on to explain that Abraham must have never revealed his earlier prophecy from Hashem about having a son, otherwise she would not have doubted the announcement that she heard from the angels. The Ramban further explained that Abraham had not told her because she was also prophetic and Abraham was waiting for Hashem to reveal the news to her prophetically. Abraham had also been very busy with the Missvah of B'rit Milah and so it's possible that he didn’t have the right opportunity to reveal such surprising news to her.
To summarize, Sarah did not realize that these men were angels and that their message was from Hashem, therefore she laughed mockingly, which she was rebuked for by Hashem. Since she had not laughed out loud she thought it would be better to deny it since Abraham was upset about it. But when she realized that Abraham knew about her laughter prophetically, she remained silent and accepted his rebuke. Abraham’s laughter was happy and therefore Yiss-haq was named after Abraham’s joy and faith in HaShem's ability to perform wonders. As Hashem’s nation, may we continue to see Hashem’s wonders performed on our behalf and when we see them we should laugh and rejoice like the verse says:
אז ימלא שחוק פינו ולשוננו רנה Then our mouths will be filled with laughter and our tongues with joy
This verse is referring to the Final Redemption which with HaShem's Mercy hopefully will take place in our days!!!