A conflict becomes harder to resolve when every concession must look like defeat.

When the only available meaning of giving ground is losing, both people will hold positions long past the point where either believes in them. It is not stubbornness exactly. No move is available that does not also cost something, so the sensible thing becomes the expensive thing. Conflicts stick here far more often than they stick on the actual disagreement.

Make a route that is not defeat. Concede something small yourself first and name it as sense rather than surrender. Say plainly that you would like to find something you can both live with, which changes what any later movement gets taken to mean.