Korach and His Group Accused Moshe of Adultery

Sanhedrin 110a:

Question: "Va'Yishma Moshe va'Yipol Al Panav" (“and Moshe heard, and he fell on his face” Bemidbar 16,4) - what did Moshe hear?

Answer (R. Shmuel bar Nachmani): They suspected Moshe of transgressing the prohibition against having relations with a married woman - "va'Ykan'u l'Moshe ba'Machaneh" (“and they were jealous to Moshe in the camp” Tehillim 106, 16).

(Rav Shmuel bar Yitzchak): Everyone formally warned his wife not to be secluded with Moshe - "va'Yikach Moshe Es ha'Ohel v'Nota Lo mi'Chutz la'Machaneh" Shmos 33,7 (the word קנוי can mean jealous or indicate the formal warning given to suspected adulteress).

Why did they think to accuse Moshe about possible actions with a married woman?

1. Marasha: The source of the suspicion is that Moshe had separated from his wife at G-d’s request. The scoffers said it was impossible for any fragile man to abstain permanently from a woman for so long, and thus, must be engaged in illicit relationships.
2. Keli Yakar: (Sotah 4b) One who is haughty will eventually stumble with (seduce) a married woman. Thus, Korach says we are all worthy and holy, so why does Moshe assume airs to be raised above all of us, and this accusation reinforced their argument.
3. Pri Tzadik: They believed Moshe received his prophecy like all the other prophets through angels called “Ishim” and not direct from HaShem. Thus, Moshe was like a woman receiving from “men” and was like everyone else, and had no reason to be raised above everyone else.
4. Sheloh: Moshe appointed Aharon as Cohen Gadol who would administrate any Sotah activities. They accused Moshe of deliberately installing his family in the Kehunah to cover up any of his possible adulterous actions with impunity.
5. Rabbi Chaim haRofe: A person that assumes a leadership role is tempted with self-benefits, and this is compared to having physical benefit from an adulterous activity. Thus, they accused Moshe of assuming leadership to obtain personal benefits.
6. Ri'af: When any member of the community had an issue to discuss, they would turn to Moshe who was in his tent outside of the camp. It is clear that women as well as men would turn to Moshe for direction, and this led to suspicion. The Torah, however, dispels any such claim by emphasizing that Yeshoshua, Moshe's protégé, never left the tent (see Shmos 33:11).
7. Margoliyos HaYam: The Ohel Moed was set up outside the camp immediately after the Sin of the Golden Calf, when the women refused to hand over their gold jewelry to build the calf. This led their husbands to suspect that they listened to Moshe more than to their own husbands, and thus, they were suspicious of Moshe’s intentions towards their wives.
8. Toras Chaim: Korach instigated the others to accuse Moshe of this action. Moshe was a reincarnation of Hevel, and Korach was a reincarnation of Kayin. A sister-twin was born with Hevel, and they argued about who was to have the sister as his wife and Kayin killed Hevel. Thus, Korach continued the quarrel and again accused Hevel/Moshe of desiring a married woman.
9. Ainei Yitzchak: Korach only believed in the first two Dibros (Anochi and Lo Yiheyeh) that all the people had heard. He accused Moshe of creating the other Dibros and other mitzvos from his own heart. Moshe applied these mitzvos to everyone but not to himself. Therefore, Korach brought the examples of Tzitzis and Mezuzah. Similarly, Korach speculated that Moshe proposed that the command of “do not commit adultery” applied to everyone else but did not apply to himself.