> How can I be legally responsible for my parents?

Well your parents are legally responsible for you for a period of time. There are many countries (I am most familiar with Germany in this regard) where the children are considered responsible for the parents. I was not aware this was the case in the USA.

In some countries it's quite difficult / impossible to disown or disinherit various relatives.

In Germany, the obligation to pay alimony depends on the child's income. Only when the childs income (before taxes) excceeds 100,000 Euros per anno she/he has to pay something. There exists no obligation to pay alimony for grandparents.

What if you're estranged from your parents? If you haven't talked to them for twenty years are you still liable?

The law provides for exceptions in serious cases. However, the German Federal Court of Justice has interpreted this quite strictly. A son who had no contact with his father for 40 years and was disinherited except for the compulsory portion still had to pay alimony. The court reasoned that the son had received substantial assistance from the father during his first 18 years and that the father had only made use of his right to testamentary freedom.[1]

Just a side note: If someone has received gifts from a person who later becomes destitute, he or she must return the gift under certain conditions (the gift was made no more than 10 years ago, the recipient was not destitute on his or her part, it was not a gift of decency such as a small birthday or Christmas present, etc.).

[1] BGH, Judgment of 12 February 2014, Az. XII ZB 607/12 (PDF, in German) http://juris.bundesgerichtshof.de/cgi-bin/rechtsprechung/doc...

In the example you mention, it was the parent that went to Greece. It was a child living in the US that was forced to pay.

It is actually worse than that. Many states also have criminal penalties allowing incarceration for financial neglect of parents.

Realistically, when parents get old, it is their children who become responsible for them. I feel like this is quite common sense... especially seeing as children inherit from their parents...

Consider that parents may have children in their mid 40s. These children are effectively dependent until ~20. Often they'll accrue significant debt to pay for college. Then 10-15 years later their parents may need significant care. If those parents weren't wealthy or careful to save then these children could find that they've few if any years free of heavy financial or caretaking burdens. Then consider they may want children of their own.

The lack of a real social safety net in the US really feels like previous generations pulling up the ladder.

> The lack of a real social safety net in the US really feels like previous generations pulling up the ladder.

At first I misread the last word as 'latter' and I was confused because it completely reverses the meaning. English is fun sometimes.

Parents choose to have a child and should have the responsibility to care for them. Despite this, there are still mechanisms by which parent can legally abandon their children. Children do not choose to be born, so the moral contract is different. I would agree that most people who were cared for as children should care for their elders, and should want to. But what if they hate or despise their parents. Do they “owe” for what the parents did despite never agreeing to the obligations.

Children do not choose to be born, don't want to sound cynical, but they can undo it quite easily. If you think about it, being born is best thing that could have happened to you. Because without it actually nothing could have happened to you. So being alive is better than not to exists at all.

Except parents can will nothing to their children if they choose? Many people inherit absolutely nothing from their parents.