The cumulative scriptural counter-argument against Baptismal regeneration centers upon the fact that water baptism is only a figure, a symbol of the true baptism / circumcision /removal of sin / putting away of the old self. The true baptism is a washing in Christ's blood which washes away sin and produces an answer of a good conscience toward God (see 1Peter 3:21, please note that the [true] baptism really saves). Of course, water baptism symbolizes not only the sprinkling of the Lamb's blood, which saves households from the wrath of God, but it also pictures the purging of sins "by the spirit of judgment, and by the spirit of burning"(KJVS Isaiah 4:4), which is the Holy Spirit's cleansing of God's elect people - i.e., regeneration and sanctification, both of which are application acts of the salvific effects of Christ's redemptive death for His people.
Water baptism is a symbol of what God does in salvation of His people in Christ. The same is true of circumcision in the times of shadows: the true circumcision was not done upon the flesh by human hands, but upon the heart by God Himself, so that the true circumcision (true Jews) are spiritual / regenerated people, who are actually identical with believers who are also circumcised / baptized by God Himself(see Philippians 3:3)
Look at Romans 2:28,29: For he is not a Jew, which is one outwardly; neither [is that] circumcision, which is outward in the flesh: But he [is] a Jew, which is one inwardly; and circumcision [is that] of the heart, in the spirit, [and] not in the letter; whose praise [is] not of men, but of God". The same can be applied to NT Christians, whose boast must be not in outward water baptism, but in true, real washing away of sins, performed by Christ Himself, which results in a new sanctified life: "For he is not a Christian, which is one outwardly; neither [is that] Baptism, which is outward by water: But he [is] a Christian, which is one inwardly; and Baptism [is that] of the heart, in the spirit, [and] not in the letter [of the outward ritual]; whose praise [is] not of men, but of God". Since the true circumcision was not done by hands, neither is the true Baptism in water, for the two signs are identical in meaning, for both point to Christ as the Redeemer and Sanctifier of His people, "in whom also ye [the NT Christians] are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: Buried with him in baptism, wherein also ye are risen with [him] through the faith of the operation of God, who hath raised him from the dead" (KJVS Colossians 2:11,12).
See, those who have been born again, have been circumcised / baptized "without hands", i.e., without the medium of human sacramentalism. Thus, though the sign (water baptism) is not without significance for it points to the true washing of sins by the blood of Christ and it is also directly instituted by Christ Himself, so the observance of this rite for believers and their children mandatory, yet it is not necessary unto salvation, no more than the sign of circumcision itself could produce the righteousness of faith, which Abraham possessed.

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For the truth's sake, which dwelleth in us, and shall be with us for ever (2Jn.1:2).