When Sarah hears she will have a baby by the angels at the age of 90 she laughs inside. She asks how old people like her and her husband Avraham will have children – at the age of 99 – him being so old.
G-d asks Avraham why did Sarah ask how will she have a child? – she being so old. Here we learn that people can change their words (ie, tell an untruth) for peace. G-d mentioned that she said that She was so old – but not mentioning Avraham being so old.
G-d asks – why did she laugh when she heard that she would have a baby. Sarah denies it – and Avraham says she did laugh.
Avraham also laughs when he hears the news. But G-d isn’t concerned about his laugh. But G-d seems upset at Sarah’s laugh.
Apparently Avraham was laughing for Joy that he would have a child after all these years. Sarah laughed because it seemed like the fact she would have a child seemed unlikely.
If G-d wanted to cause peace between the couple – why does He bring up this fact to Avraham that she laughed.
One reason is because either G-d wanted Sarah to correct herself – to have the proper Torah perspective – that she laugh should have been a laugh of Joy – not a laugh of skepticism.
Perhaps also that G-d wanted Avraham to correct this Middah (character trait) of skepticism in himself as well that caused it to manifest itself in Sarah.
It’s good for us to understand why react in a particular way. It behooves us to improve.