Baptism and Circumcision
Central to my critique of the covenantal argument for infant baptism is that it fails to understand correctly the proper relationships between the biblical covenants and the degree of continuity and discontinuity between them. Pedobaptist rightly emphasize the unity and continuity of God’s salvific plan across the ages. They fail to do justice, however, to the progressive nature of God’s revelation, especially regarding the biblical covenants, the covenant community, and the covenant signs. In the end, this leads them to misunderstand the proper degree of discontinuity inaugurated by Christ’s coming and to which the Old Testament points, namely, the arrival of the promised new covenant age. (Wellum, 'Baptism and the Relationship Between the Covenants')
Many Pedobaptist view the Abrahamic covenant essentially identical with the new covenant and group them together and call it the "Covenant of Grace", same covenant just different administrations. They downplay or ignore the national and typological aspects of the Abrahamic covenant then apply the genealogical principle "you and your seed" to the new covenant.
Who are the people of God? There are differences between the new covenant people called the Church and the old covenant people called Israel. And these differences explain why it was fitting to give the old covenant sign of circumcision to the infants of Israel, and why it is not fitting to give the new covenant sign of baptism to the infants of the Church. The Church is not a continuation of Israel as a whole; it is a continuation of the true Israel, the remnant—not the children of the flesh, but the children of promise. Rom 9:6-8 6 But it is not that the word of God has taken no effect. For they are not all Israel who are of Israel, 7 nor are they all children because they are the seed of Abraham; but, “In Isaac your seed shall be called.” 8 That is, those who are the children of the flesh, these are not the children of God; but the children of the promise are counted as the seed.
God's promises were made to Abraham, Isaac and Jacob as believers and they were the spiritual food and property of none but believers (Rom 4:13,16) (Pink, "The Divine Covenant")
Pedobaptist teach circumcision and baptism are essentially the same ordinances. But there are major differences. 1) Circumcision was administered to only male physical children, Pedobaptist baptize male & female children 2) Pedobaptist require the child to have at least 1 believing parent, Circumcision was administered to male babies if their parents were believers or not. 3) Circumcision creates physical evidence (a Mark) that stayed with the male child his whole life, Baptizing a baby is just a ceremony like the baby dedication that some churches do. 4) Circumcision was only for the Hebrews, Baptism is for believers worldwide. 5) Circumcisions' is physical, your relationship to Abraham; Baptism is spiritual; your relationship to Jesus Christ
There is agreement among most Pedobaptist and Credo Baptist (Believer Baptist) that when a person is given faith and he has not been baptized the Bible commands that person to be baptized. This is a public declaration of an inward transformation. Baptism celebrates not what the believer did, come to saving faith, but what God has done regenerated another helpless sinner, indwelling them with the Holy Spirit, creating a new creature that is equipped to honor God, adding them to the church, adopting them as a beloved child and Imputing Christ’s active obedience, Justifying them before a Holy God.