Every person born in the US was once a child, not having children in no way makes you more responsible, it just makes you opting out of a major part of society, which is a fine personal choice but if this was implemented when you were a child you would have benefited the same as anyone else.
Also, other peoples children WILL be taking care of you when you are old ,because they will be the doctors, firefighters, manufacturing line workers, delivery drivers and everyone else that carry out services that you will still need. They will also be contributing to the tax base that provides social services (social security is paid for by the current generations tax revenue not the original contributors', as bad as this is)