According to paedobaptists, what justifies a link between circumcision and baptism since both males and females are baptised?

The particular view that raises a query in my mind is this, as fully detailed in my answer to this related question, https://christianity.stackexchange.com/questions/91006/according-to-reformed-theology-how-can-one-justify-infant-baptism/91065#91065 After detailing why the sign of the Abrahamic covenant (circumcision) has its counterpart in the sign of Christians in the New Testament (water baptism), the author I quote (*A Faith To Live By*, p210, Donald Macleod, Christian Focus, Mentor) says: > “The children of believers continue to have the same special > relationship to the covenant as their Old Testament counterparts had; > and, consequently, the same right to the covenant sign. Why do I > baptise children? ...It is because God gave me an ordinance: Put the > sign of the spiritual covenant on the physical seed.” My query is that although 8-day-old babies were to be circumcised as a sign of that Abrahamic covenant, that only applied to male babies. ***No female babies were ever circumcised. Yet Christian water baptism is administered to both males and females (irrespective of their age). Is this not out of sync with the physical sign?*** Further, the author speaks elsewhere in his book about how, > “when a man comes to faith he may embrace his children with himself > under the sign of the covenant”, and “we should not give the sacrament > of baptism to a man for his child unless we would be prepared to give > it to him for himself.” (*Ibid.* p 219 & 220) But what about a woman coming to faith, who seeks baptism, and she has children? Is it only a female – like myself – who notices a need to consider females a bit more regarding the theology of baptism? *Disregard that last question if you don’t think it helpful.* *My question is,* **Given that no female babies were circumcised as a sign of the Abrahamic covenant, why are female babies of Christian believers given the sign of the new covenant (water baptism)?** *Edit to clarify what my question is NOT:* it is ***not*** asking why females are baptised given that they are not circumcised. To clarify what my question IS: it ***is*** questioning the claimed link between circumcision as a sign of the old covenant and the claim that water baptism is a corresponding sign of the new covenant. ***There seems to be something out of sync with this claimed link.***