The Gemara in Megillah (13b) says that when the goral [lot] landed on the month of Adar, Haman was pleased because this month was not favorable for the Jewish people since Moshe passed away on the seventh of Adar. However, he was not aware that Moshe was born on that same day.
How is it possible that Haman, who knew the date of Moshe’s passing, should not know the date of Moshe’s birth?
For a peshat from the Meshech Chochmah see Dvar Torah below titled “A Beautiful Peshat from the Meshech Chochmah”.
R’ Yonosan Eibshitz (Yaares Devash Vol. 1, Derush 3) offers an alternative peshat: The Gemara in Kiddushin (72b) says that before a tzaddik leaves this earthly world, a new tzaddik is born who will replace him, and according to the Arizal there are sparks of Moshe in every generation embodied in that generation’s leader. Haman actually knew that Moshe was born on the seventh of Adar; however, since he died on the seventh of Adar, he considered this a “cut-off period” for Klal Yisroel. He did not know that when one tzaddik leaves this world, a new tzaddik - a new Moshe - is born to replace him and that Klal Yisroel will be victorious over all their oppressors in his merit.
This explains a difficulty in the wording of the Gemara, “He did not know that on the seventh of Adar he (Moshe) died and on the seventh of Adar he was born.” Since a person is born before he dies, it should have said the reverse, “He did not know that he was born on the seventh of Adar, but he knew that he died on the seventh of Adar”?
Haman, indeed knew that Moshe was born and died on the seventh of Adar; he did not know, however, that when Moshe died, on the seventh of Adar, another Moshe, i.e. leader and tzaddik, was born on the same day.
In fact, Mordechai was a gilgul [reincarnation] of Moshe and according to the Medrash Rabbah (6:2), Mordechai in his generation was equivalent to Moshe in his generation, and they shared many similar experiences during their respective lifetimes.
Alternatively, R’ Yonosan Eibshitz suggests: Moshe was indeed born on the seventh of Adar. However, the Torah relates that: “She (Yocheved) hid him for three months” (Shemos 1:2). Thus, when Basya found him floating in the water on the twenty-first of Nissan or the sixth of Sivan (see Sotah 13b), it was assumed by all that he was recently born.