Im assuming that when you say a "Nursing home" you actually mean a residential home? very different.
A nursing home has on site nurses for nursing care, a residential home is where old people live that need a bit of help in there later years but not nursing care.
Actually im probably being a touch pedantic but that is the difference between a Nursing Home and A Residential home, A residential home does not require any qualified nurses on its staff.
And what will the world's population be then? It's ridiculous - people have to die! We can't all just keep trundling along for hundreds of years. I wouldn't want to anyway, especially seeing how grumpy some folk can get past the age of 60 - what would they be like at 120?
If you managed to banish the problems with aging then you'd probably be fit enough to stay in charge, and prevent all the things otherwise imposed on you that make you grumpy. Well at leeast until you are 120.