The purpose of argument is to convince the audience.  That is all.  That is the only purpose.  It is never, ever the purpose of argument to convince your counterpart/opponent (i.e. the person with whom you are arguing.  To argue is to adopt a partisan position.  The function of the brain is not to identify truth, but to secure survival, and in an argument, survival is secured by winning the argument in the eyes of tribal onlookers; therefore an arguer will bend all of his faculties to winning the argument, regardless of the truth of his position.

Some people may, in rare cases, argue to test and refine their partisan positions, and such people may adopt this as another reason to argue.  If so, good.  But for most, arguing without an audience is a waste of breath.

Like you, the other person holds his position not as a result of a dispassionate reasoned analysis but as a result of his psychological development from infancy.  If your goal is to change your counterpart’s position, you will fail.  If your goal is to help your counterpart change his position, argument will not accomplish that.  What you need to provide that person is not argument but therapy.