There is no reason to point out that people of both genders were now receiving the sign of the covenant, except to contrast it with the old sign of the covenant. Implied in this contrast is the fact that baptism had replaced circumcision. Spiritual Circumcision There were Judaizers in the church who wanted Gentile converts to be circumcised and to follow the whole Mosaic law. That is, they have already received that inward circumcision, that spiritual cleansing of the heart, that is effected by the Holy Spirit. In either case, another contrast with circumcision is in view.
Physical circumcision removes a small piece of flesh.
Paul's opponents might well have agreed that an inward cleansing was in order. However, they would have insisted that this be signified by physical circumcision. Physical circumcision has nothing to add. The Abrahamic covenant is fulfilled in the new covenant, and circumcision has been replaced by baptism as the sign and seal of the righteousness of faith. Children in the Church Under the Abrahamic covenant, those who were born within the covenant community received the sign of the covenant as infants.