Parents are already mandated by the state to take care of their children, right? So why is it a big leap to mandate that children take care of their parents.
In the vast majority of cases, parents voluntarily had sex knowing that it could possibly lead to the creation of a child. They knew they might be legally responsible for caring for a child for 18+ years and that the child might have special needs, and they chose to accept that risk.
Children, on the other hand, do not choose to be born. They don't have any choice in who their parents will be or how their parents will live their lives. It isn't just for the government to FORCE children to be responsible for a situation they had no control over, even if the decent thing for the kids to do is to take responsibility anyway.