While what Cathymac77 says is accurate to the text, one should consider that Tom and Myrtle are from VERY different worlds. Tom is from "fashionable" East Egg while Myrtle exists in the Valley of Ash. For him, this is another fling from which he can (and will) conveniently retreat to his sham marriage to Daisy. For Myrtle, this is the promise of a better life, with the inconvenient impediment of "Daisy being Catholic"--which she is not--(not allowing divorce). She cannot not see Tom for what he is, a jerk, and not her knight in shining armor.
While the drinking is certainly a contributing factor, as is Myrtle mentioning Daisy's name, Tom is bored at this party as indicated by his snubbing of Myrtle's artist neighbor and her friends. They are just too different.
The quarrel is a literary trick to develop Tom's (and Myrtle's)character for readers and to further differentiate the rich from the poor. He is violent ("a brute") and entirely mysogynistic. By contrast, Myrtle is shallow (the "Town Tattle" magazine) and hopelessly romantic--"You can't live forever"--but stupid.
This division makes the relationship impossible and inevitably leads to his violence and the tragedy that is to follow.
*Quoted material is from Chapters 1 and 2 of The Great Gatsby.
Tom and Myrtle are having an affair. They have been having a party and there was drinking involved. Myrtle starts to become very loud and obnoxious as she drinks more and more. Tom gives Myrtle a puppy as a gift and when he does, Myrtle starts to talk about Daisy, Tom’s wife. Tom is very adamant that Myrtle is not to mention Daisy….his wife. Because she’s been drinking, Myrtle tells Tom that she will do whatever she wants, when she wants. She’s very angry. She begins to say Daisy’s name over and over and over again. Because of this, Tom loses control and breaks her nose. Needless to say, the party is over very abruptly.