How do you answer a person with dementia who doesn't believe you?

When my mom was in that stage, I would say, we can go after dinner (or lunch, or in the morning)... Redirect with other activity if possible. You can also ask, what are you going to do when you get home? Arguing never works ;-) 

I think "home" means different things at different times... Remember that as the brain is affected, word recall is impacted. "Home" is usually a place of peace and safety and comfort... That may be what she is looking for. Some people with demensia are living in the past and are looking for the "home" of an earlier time. 

When mom is agitated, whether it is she wants to go home, or another issue, I try to acknowledge her frustration (validate her feelings) and if I see a trigger, fix that, if not I try to redirect...."I know, it would be nice to see your mommy...I will see what I can do about that... Let's have some ice cream."

Lnisse, usually when a person has dementia is asking to go "home", they really mean their "childhood home" where life was happy and easy.   You can tell the person "maybe we will go tomorrow" and leave it at that. 

There are some cases where an elder will say they want to go home, they mean "home to the Lord".

An older friend whose husband with Altzheimers insisted on going home, agreed with him, took him out the back door, walked around and entered the front door telling him they were home. He was happy with that.