You weren't arguing about specifics; stop focusing on them.

You were arguing about morality, personal beliefs about the kind of people you should be, or what kind of world you want to live in.

The inconsistencies in their argument don't matter.

The inconsistencies in your argument don't matter.

What does their argument say about their view of the world, people, or the problem you’re facing? 

How can you empathise or make their argument with this in mind?

This isn’t a game to be won. It’s a person to be understood. It’s a puzzle that’s a joy to solve. 

If you were arguing their position, what would you say?

Have you found the key ideological difference yet? What different moral position did they have? What different context did they have that you don’t?

Don’t re-enter a conversation until you know what the key difference is. Use their worldview as a framing. Maybe you actually agree with them now... or at least you understand why you don't and respect why. We’re just monkeys after all. 

Discuss the basic beliefs you have, and confirm theirs. You’ll end up in a better place, at least a more understanding one. 

Specifics are the death of a good discussion; they are not what you’re really arguing about. 

It’s Never About The Specifics