Both parties are responsible for her support. Not just one. Personal responsibility applies to them both.
Agreed completely, but for him to ask for her to give him money is just not what a man should do IMHO. She has the money to raise that little girl on her own if she chooses to, why is there a need for either one of them to sponge off the other?
They should both be responsible for the child’s support, but he shouldn’t be claiming child support for joint custody. Why should she have to pay him.