There have been some very well-thought out and sensitively given answers in this thread.
In answer to your question, should we automatically care for our parents in old age, I would say yes, of course. But I think there are a number of ways which that care can manifest itself, and not all of those options involve taking your adult parent into your own home. Sometimes residential care can be the best option, and I think it can be terrible for the adult children who are sometimes made to feel guilty by the more quick-to-judge members of society, who assume that placing the parent in a care home means they don’t care themselves, or couldn’t be bothered to make space in their own lives for that parent at their time of need. I don’t deny that this may be true for some people (sadly), but I believe that for the majority of people who have positive relationships with their parents, making the decision to place a parent in a residential care home is absolutely harrowing, done as a last resort, and done with love for that parent, and keeping their best interests in mind. In some cases, as others have said, for some people and in some situations, it is the most caring, dignified and kind solution. As @JLeslie said, I think it is of the utmost importance to consider everybody’s wishes in this situation.
I am the granddaughter to several grandparents (one pair are aged 93 and 91, and the other grandmother is 89). My 89-year-old grandmother who lives alone, in the last 15 years, has suffered the sudden death of my grandfather, knee replacements, a hip replacement, a severely broken thigh bone, cancer of the tongue (her tongue was replaced with part of her forearm, which was replaced with some tissue from her leg, and whilst she is cancer-free now, she cannot eat solid foods or taste food properly), severe arthritis, osteoporosis, vision problems, and now, some early signs of dementia (intially calling family members by the wrong names, but now, forgetting conversations and having them repeatedly, etc).
She chooses to live alone (although she has a hot meal delivered to her daily) and is housebound (she requires the help of others to get out and about). A few years ago my uncle and father were looking into care homes for my granny, but they didn’t find anything that met their requirements. I honestly believe that a residential home of high quality, that allowed her to live with dignity, freedom and peace of mind would be the kindest thing for her, as I think the increased social interaction would benefit her, and knowing that people were on hand to help 24-hours would really improve her confidence to try things – she is currently (understandably) very nervous about her mobility. She lives on the other side of the country from my father, and whilst we try to have her to stay regularly, it would just not work for anyone if she lived with him full-time – there are a huge number of practical reasons that would inhibit this that I won’t bore anyone with. Having said that, I think the biggest reason for her not coming to live with us is that she simply wouldn’t want it. I know she would hate to think that the youngest members of her family were putting their lives on hold, or giving things up for her comfort, even if we told her this wasn’t the case. So we do what we can to support her as best we can, even though it doesn’t involve having her come and live with my father.