Amanda Marcotte has already done a fabulous job outlining why Pope Francis was wrong to dismiss those of us living the child-free life as shallow, future bitter types. But besides misjudging those who consciously choose not to have children when they are not financially or emotionally ready to be good parents as selfish, the pope’s argument has another flaw: the idea that having children is a surefire way to avoid loneliness later in life.

“Being lonely has little to do with having children,” said Dr. Bill Doherty, professor and director of the Marriage and Family Therapy Program in the University of Minnesota’s Department of Family Social Science. “Single parents in particular can feel quite lonely for adult companionship and love, and parents with adult children who emotionally abandon them can feel acutely lonely.”

Although abandonment by adult children is likely the fear of every parent, and therefore rarely discussed in polite company, it happens plenty. The problem became so pervasive in New York that in 1981 The New York Times ran an article on the increasingly common practice of family members abandoning senior citizens in city hospitals. “In some instances, family members will give a false name and address,” the paper reported. “In others, they may call an ambulance to take the patient to the hospital alone and then, when there is no medical reason to admit them, refuse to take them back home.”

Today abandonment of the elderly can take different forms. After learning how many senior citizens in nursing homes never have any visitors, former nurse Susan Zador founded the California-based volunteer organization Visiting the Lonely Ones. “One of the directors of a local nursing home said 85 percent of his residents had no visitors,” Zador told The Daily Beast. Now program volunteers visit nursing home residents who otherwise wouldn’t have visitors. Zador is hoping to raise the funds necessary to expand the program nationally.

Many of these men and women have adult children, she said. So why don’t their children visit? “These days people are very busy with their own lives,” she said, “and now many family members live in different states.”

Dr. Jeff Gardere, a family therapist, said fear of being mistreated by an adult child one day comes up in various ways with his patients. “Those who already have children state that they are raising them in a certain way so that they will be responsible as adult caregivers later on,” he said via email. “These parents already know they want to avoid living in isolation or in adult homes for seniors.”

And yet even for the most well-meaning parent, there are no guarantees. A number of cases of adult children accused of mistreating elderly parents have made headlines recently. One of the most famous involved the New York City socialite Brooke Astor, whose senior-aged son was convicted of taking financial advantage of her and allowing her to remain in deteriorating living conditions.

Then there are the adult children estranged from their parents, who one day will be elderly and require care. A recent New York Times article profiled parents estranged from their adult children. While in some instances the grievances were clear-cut and therefore the estrangement was not entirely surprising, in other instances the parents were caught off guard and stunned at being cut off.

In one case, the mother has just one child, a daughter from whom she has become estranged. So, despite following the pope’s recipe for avoiding loneliness, she is entering her twilight years hardly different from the child-free. But while most of the latter have a lifetime to prepare for what their senior years will look like without adult children, adjusting to that reality will be tougher in her case.

But even before adults enter their senior years, children are not a surefire way to inoculate against loneliness. I know of divorced people who struggled during holiday seasons because custody arrangements meant they would have to endure at least one celebration that did not include their children. Such an experience can prove lonely for those who have come to associate Christmas with the boisterousness of children unwrapping presents or Thanksgiving with tweens helping with the turkey.

The bottom line is there are no guarantees.

Of course, having children just to have someone to be there for you when you’re elderly is not the foundation on which a healthy relationship is built, says Dr. Gardere. “Clinically, I think you should have a child only to offer it love and guidance and to reach its potential as a human being,” he said. “I think it is selfish to have a child only to have a caregiver later in life. I think that is quite narcissistic to do something like this. This is a tremendous burden placed on the child as they are growing up, and that child may become resentful.”

At the end of the day, expecting any other person to save you from loneliness may be a losing proposition, says Dr. Doherty. “In general, loneliness is more a personal predisposition than an objective social condition,” he said. “Like being a parent or not.”