Hell, your parents took care of you and sacrificed, why can't children return the favor? Besides, how could you not feel a responsibility to care for your parents when they're elderly? Everyone with parents has that obligation. Just some are able to care for them on their own, while others can't and have to resort to a home.
Every story is different, but in most cases, people nowadays bring children into this world because they feel like it. They don't take care of you because they are very nice, although may be they are. They are also not doing you a favor. In fact in bringing you into this world they contract the huge moral (and legal) obligation to take care of you and provide for you. They never asked you if you wanted to be in this world. Taking care of you is the least they can do.
Of course if parents do a good job and have nice enough children, the latter may feel the responsability to take care of their parents. (If they can, it occurs to me that when you have children you should be first sure that you can support them, not all children can chose jobs, finances and time to accommodate parents needs)
I thing it is a nice thing when children take care of their old ones. But this is not a give and take situation. The love for your children should be unconditional (at least, that's what you are always lead to believe) You cannot compare the obligations of parents toward their children with the obligation of children toward their parents.
