If you're talking to your spouse and the tension between the two of you escalates and there is nothing that you can do to make your spouse see your point of view, then I would stop any further talk because it is futile.
If he is so upset, then his feelings will cloud his rational judgement. And if you become upset too, then your feelings will cloud your rational thinking. So rather than push and push on both sides, it's better that one of you withdraws before the situation spirals out of control.
The time-out, gives both sides an opportunity to calm down and gather their thoughts and think more rationally.
After some time, once everything has calmed down, then you can attempt to open up a new discussion.
That is what I would do if faced with the situation you described.