(Mishnah - Beis Shamai): One may divorce his wife only if "he found in her Ervah (immorality)";

Beis Hillel say, even if she burned the food, he may divorce her - "he found in her Ervas (or) Davar (a matter)";

R. Akiva permits even if he found a prettier woman - "if she does not find grace in his eyes."

(Gemara - Beraisa - Beis Hillel): It says "matter" (it is permitted even if he did not find Ervah)!

Beis Shamai: It says "Ervah"!

Beis Hillel: Had it said only "Ervah", we would agree. Had it said only "Davar", one might have thought that one divorced due to a Davar (e.g. burning the food) may remarry; but one divorced due to Ervah may never remarry;

Therefore, the Torah needed to say both.

Question: What do Beis Shamai learn from "Davar"?

Answer: They learn a Gezeirah Shavah "Davar-Davar." Just like we need two witnesses for monetary or bodily punishment, also to forbid a woman to her husband due to adultery.

Beis Hillel: If so, it should say "Ervah b'Davar"!"

Beis Shamai: The way you learn, it should say "Ervah or a Davar"!

Beis Hillel: The construct form "Ervas Davar" suggests that we learn both.

(Mishnah - R. Akiva): Even if he found a prettier woman...

They argue about Reish Lakish's teaching.

(Reish Lakish): The word 'Ki' has four meanings: 'if', 'perhaps', 'rather', and 'because';

Beis Shamai explain "she will not find grace in his eyes because he found Ervah in her."

R. Akiva explains "whether she will not find grace in his eyes, (or) if he found Ervah in her."

Question (Rav Papa): If he found neither Ervah nor a Davar (such as burning the food) and divorced her, what is the law?

Answer (Rava): Regarding one who raped a woman, it says "he may not divorce her his entire life." (If he divorced her,) for the rest of his life he is commanded to remarry her;

Here, it does not say that he must remarry her.

Question (Rav Mesharshiya): If a man cohabits with his wife, intending to divorce her, will he be punished (b'Yedei Shamayim)?

Answer (Rava): Yes! "Do not plan evil against your companion who trusts you."

(Beraisa - R. Meir): Just like people have different natures regarding food, also regarding women;

Some people spill out their wine if a fly fell in. This corresponds to one who locks his wife in the house, so she won't speak with other men;

This was the conduct of Papus ben Yehudah. (It caused enmity. His wife was Mezanah, and she gave birth to Yeshu.)

Most people remove a fly that fell in the wine. Correspondingly, a normal man allows his wife to speak with her relatives;

Some people suck the food off a fly that fell in their food. This corresponds to an evil man who does not protest when he sees his wife go out with uncovered hair, weave in public with her elbows exposed, or bathe with men.

Objection: This cannot be! (No one would let his wife bathe with men! Alternatively, the lewdest woman would not do so! Alternatively, this shows that she was Mezanah, surely he must divorce her.)

Correction: Rather, she bathes where men bathe.

It is a Mitzvah to divorce such a woman - "he found in her Ervah... he sent her from his house, and she married a different man."

The Torah calls her next husband "different", for he is unlike the man who divorced her. The former expelled evil from his house, and the latter brings evil into his house.

The next husband deserves to be punished for this. If he merits, also he will divorce her. If not, he will die in her lifetime - "if the next husband... will divorce her... or die."

(Rav Yehudah): "For he hates, he sends" - one who hates his wife should divorce her;

(R. Yochanan): This teaches that one who divorces his wife is hated.

They do not argue. R. Yochanan discusses one's first Zivug (destined spouse), and Rav Yehudah discusses his second.

(R. Elazar): The Mizbe'ach cries over one who divorces his first wife - "the Mizbe'ach cries... because you betrayed your companion, the wife of your covenant."