My dad lives alone & wants to shift home care agencies. I wish to keep in my house with proper nursing and he denied. Is it a mental problem?

Not necessarily. Most people want to stay in their homes as long as possible. If he can afford home care then let him go that way. Changing agencies at this point may not be a good idea with the virus though.

Be glad he doesn't want to live with you. There are members of this group that now wish they didn't bring a parent into their home. And now, they can't get them out. A few the parent expects everyone to wait on them. Wants the childs undivided attn. To the point the child and spouse can't go out without parent whining.

He is free to make the decision to stay at home with paid help. That doesn't indicate a mental illness, it indicates a desire to stay independent and not impinge on your life.