Why do Michael and Penelope not let Alan and Nancy Cowen leave their house?

Firstly, thanks for your question. The movie Carnage by Roman Polanksi has been one of the most beautiful representations of human nature and the intricacies of the invisible shroud we cover ourselves with. It is a movie adaptation of the play "God of Carnage" by Yasmina Reza.

To start with here is a direct quote from Polanksi about his characters:

In an interview with Le monde, Polanski described his interest in the movie: “Carnage is a story about two couples who have friendly relationships in the beginning, then it completely deteriorates into insults and hatred. This is what appealed to me in Yasmina Reza’s play. It is the denunciation of the politically correct. The characters reveal their true human nature, that is, they are capable of hating, of being selfish, though everything is concealed under a middle-class veneer of people who want to be respectable.”

In almost every gesture of the Longstreet Family, at the beginning, we would see a genuine endeavor to be polite, well mannered, respectful and welcoming as much as they could.

Here is a dialogue of Michael when the first time, the Cowens start to leave

Source : https://www.wsws.org/en/articles/2012/02/carn-f10.html

Michael: "I didn't mean to rush you out. Here here"

Call it the plot of the play or mere chance, every time the Cowens approached the lift lobby to leave, the conversations went to an unexpected level of hostile candidness.

Towards the later half of the play/ movie we also find Penelope arguing with Michael and eventually asking him, why does he feel so inclined to "mitigate" things.

Penelope: You're always mitigating. Your'e trying to reconcile everything.

Michael: I am not!
Penelope: You are!

From these we do find a notion that unlike Penelope, Michael, right from the start, was more dedicated to uphold the Longstreet Family manners and warmth.

There are innumerable citations of Character Analysis all over the internet but almost all of them say this part in a gist. Here, John C Reilly, himself talks about his characters and the other.

My answer would be: As everyone tries to present the best version of themselves at the beginning and due to this nature of Michael's Cowen's character, he somehow feels compelled to show the warmth or manners for the Cowens as they were after all their guest.