The point which you have avoided is that the adults are adults (responsible) and the child is a child.
Clearly, in the matter being discussed the female adult is not responsible in more ways than one. It is obvious that the child has a biological parent. If she wants to receive child support she should track that man down and get it from him. She should not be lying to the man she claims to be the father and she should not be lying to the courts about who the father is so as to collect child support from the lied to man.
There was a 15 year old kid in Mass. last year whose girlfriend became pregnant. Thinking he was the father he took full responsibility, got a job and upon birth started paying child support. Shortly after that he questioned the mother about who the father was after he heard talk of him not being the father. She said he was and he demaned a paternatiy test. It showed he was NOT the father.
He then sued her in court to remove his child support responsibility. The court ruled that he MUST continue to pay child support AND PAY FOR THE KIDS COLLEGE EDUCATION!