Hello Redhead and welcome
What you described is very typical of Alzheimer's behavior. It is the progression of the disease you are seeing. Yes, you might be able to win him over in a moment of intense convincing... but is he really won over or just saying ok because you don't understand his point of view? Even if he does get it in the moment he forget it quickly and goes back to what his brain is telling him. Either way to constantly argue with him is only aggravating both of you. If he doesn't remember or understand... and it's not life threatening then leave it be. Also know that you are not going to be successful in making him remember. His brain is telling him something very different and his reality (as warped as you might think it is) is as real to him as your reality is to you. You telling him it is his house is just as bizarre to him as him telling you that it is not his house! Since we are the rational thinking ones... we have to join in their reality rather than trying to drag them into ours.
Instead acknowledge the fact that he is upset. Ask him what is bothering him about where he is. Try to connect with him rather than telling him he is wrong. Validating his feelings will go a long way. I he knows you have accepted that he is uncomfortable where he is then you might find out what can be done to make it better for him. Being argumentative will only deflate him and make the situation worse.
Wandering is a very real possibility at this point. Trying to convince him that he is home is NOT going to change that fact. He gets up in the middle of the night and Mom is sleeping... and he decides he has to go... he's gone. It happened with my Dad and it is very scary knowing they can not function in that world out there but they are in it. It is a life threatening situation but once again, you can not stop it by trying to convince him to stay home
What you can do is alter the environment to accommodate the possibilities.
If your house has a single pathway to exit the house you can put in a motion sensor. It will alarm if they wander at night and wake you up. Install dead bolt locks that you have to have a key to open. Then put the key OVER the door or in a location that you will find but not him. His vision is probably narrowed to the point that his peripheral vision is impaired and he will miss things up high. Make sure he has on an emergency ID that indicates he is cognitively impaired and who to call. I have seen people do other things as well. One family hung curtains over the door. Their loved one couldn't find the door because it was hidden from view. Another put a black rug in front of the door. Their loved ones depth perception indicated the black was a hole and they would not cross the black rug. Another friend hung wind chimes in the door way. It alerted to any attempt to exit. But you do need to do something before it happens....
That is one of the major reasons my Mom and Dad could not stay at home. Their house had five doors and you could only see two from any single location in the house. Mom (Alzheimer's) would be going out the front while Dad (Vascular) was going out the back. Occasionally, Dad in particular didn't remember it being "home". Other times he needed to go do something that related to one of his delusions. Mom would just "run away". They even eloped (official term for wandering) from AL. That is why they both ended up in a locked dementia unit.
So be very vigilant concerning wandering. Have an honest discussion of the problem with Mom. It may be time for additional help.