If you show something is wrong in the reasoning of someone, even if the person agrees immediately, first you'll get: "Yes, but ... bla bla" or, "That's because ... bla bla."
We have been trained from childhood to make excuses. We are so good at it. The excuses must get out. So, first let the excuse get out, then just wait for the person (perhaps silently) agree, and then discuss what we can do about it.
If we immediately react on the first reaction, we escalate on a path we both don't want to be. Fortunately I haven't been through a divorce, but in my imagination a lot of divorces go like this. Someone says something, and the other immediately replies, upon which the first immediately replies.
So the advice is to try (I know how difficult it is!):
Let the excuse come out and wait for the next reaction.