I have been a certified nursing assistant for the last six years. I have worked with the elderly, with Alzheimer's suferrers, and with developmentally disabled.
There is no such thing as an "old age" home, at least not in the US. We who care for them are medical professionals, some are nurses, most are certified nursing assistants.
What we do is called LTC, or long-term care. We do not refer to the people we care for as patients, though that really is what they are. But we deliberately de-emphasize the medical image because we want the people we care for to feel our place is their home (which for most of them it is).
We call the elderly patients residents, the developmentally disabled clients.
Our clients and residents are not in our care because their families chose themselves over their loved one. They are in our care because they require medical care, which their families cannot provide. They are better off in our care.
Not all elderly live in a nursing home because not all of them need it. None of our residents/clients are in our care because their families did not want them anymore. It is not necessarily your choice either. If you cannot provide proper long term medical care for your parents, Social Services may even force you to place them in a nursing home.
By the way, we are not strangers. Nobody works in LTC because it is "just a job." We tend to be overworked and underpaid. We do it because we get attached to our residents and clients: They are like family to us.
If the day ever comes that your parents require long-term care, please do not feel you are getting rid of them so you can live comfortably. Quite the contrary, if you really love them, you will provide them with all the care they need, when they need it, even if that means placing them in a nursing home.