לזכות רפואת דינה ברכה בת אסתר הדסה בתוך שח"י 

Why did Sarah laugh when she heard she was going to give birth? She didn't WANT to believe that she would become young again and give birth b/c then the ליצני הדור would say that Avimelech is the father [which they actually did]. If she remained old and an open miracle happened and she gave birth, then people would understand that Avraham is the father. But if she gets her period and returns to her youth they would ascribe the fetus to Avimelech. Hashem answered "היפלא מה' דבר" - Meaning, אין לך עסק בנסתרות. How I do miracles is my business and not yours.  

The reason Hashem wanted it this way is that when big things are happening they must be hid from the forces of evil, the Dark Side. That is why Avraham came from Terach - מי יתן טהור מטמא. Someone so pure came from such impurity. That is why Moshiach was produced [on his mother's side] in the cave in an incestual relationship between Lot and his daughter and on his father's side from the problematic union of Yehuda and Tamar. Yitzchak is unusually holy. An עולה תמימה. His ashes are on the mizbeach as if he was slaughtered. He was never allowed to leave the confines of Eretz Yisrael. He doesn't take a שפחה like his father Avraham and son Yaakov but davens for a child when his wife is barren. Holy-holy!!!  The Sitra Achra doesn't like such things. So Hashem made it that people would say that Avimelech is the father. That keeps the Sitra Achra at bay. He doesn't appreciate the Kedusha and thus won't obstruct it.  [עפ"י תורת מרן הרב חרל"פ זצוק"ל]

What did the ליצני הדור want to say when they relate Yitzchak to Avimelech. So what!! What does it matter who his father is?? The pasuk says that Avraham will teach his children to follow "דרך השם" which means [Rambam] that they will walk in the path Hashem Himself walks on כביכול [and not as we would think that they followed the path that Hashem commanded them to follow]. That means that in order to be a Patriarch of the Jewish people one has to embody a Divine trait in order to emulate the Divine. So Avraham's chesed and Yitzchak's yirah were both expressions of their desire to follow in the "דרך השם". If they would not have both had this approach then there would be no Jewish people. So the ליצני הדור say that Avraham is not Yitzchak's father meaning that there is no synergy between the two Avos who both followed דרך השם b/c in fact they weren't related. That means ח"ו no Jewish people. ליצנות is not humor but devaluing important values. The greatest ליצנות is separating between Avraham and Yitzchak b/c that is the dismantling of the Jewish people.  [מרן ראש הישיבה זצ"ל]