Your child is a U.S. citizen; what they need is evidence of his/her U.S. citizenship. Your passport(s) are not directly necessary for that. What you ultimately need to prove is: 1) You (or the other parent, or both) were a U.S. citizen when the child was born, and 2) if only one parent was a U.S. citizen when the child was born, then that parent was physically present in the U.S. before the child's birth for 5 years, including 2 years after turning 14.
The item you cited is listed under "Evidence of parents’ U.S. citizenship". So basically, they want you to prove that you were a U.S. citizen when the child was born, and any passport that was issued before the child's birth should suffice. But a passport is not strictly necessary for this (imagine if someone lost all their past passports; obviously, it doesn't mean they're doomed). If you can present a U.S. birth certificate (if you were born in the U.S.) or Certificate of Naturalization with naturalization date before the child's birth (if you were naturalized) or Certificate of Citizenship or CRBA, any of those would by itself be sufficient proof of your U.S. citizenship.
The checklist is probably overly general because they would rather have too much evidence than not enough, and the cases of citizenship are so complex that it would be confusing to list out what is needed in different cases, so it's better to request everything that might possibly be needed.