"For Christ also suffered for sins once for all, the righteous for the unrighteous, so that He might bring you to God, having been put to death in the flesh, but made alive in the spirit; in which also He went and made proclamation to the spirits now in prison, who once were disobedient, when the patience of God kept waiting in the days of Noah, during the construction of the ark, in which a few, that is, eight persons, were brought safely through the water. Corresponding to that, baptism now saves you—not the removal of dirt from the flesh, but an appeal of a good conscience to God—through the resurrection of Jesus Christ, who is at the right hand of God, having gone into heaven, after angels and authorities and powers had been subjected to Him." 1 Peter 3:18-22
Clearly, water baptism does not save us. How many people have been baptized as children or as adults only to turn their back on the faith and walk away from it? Catholics may believe these people are saved, in spite of them living like the Devil, but hopefully most of us do not. If baptism actually saved, then what explanation do we have for this? Contrary to what Charismatics believe, you cannot lose or forfeit your salvation, because it is not of yourself to begin with; it is a gift from God. Yes, these people apostatized, but, no, they were not saved; and water baptism certainly did not save them.
First, the baptism being talked about here has nothing to do with water. That is clear from Peter's words, "not the removal of dirt from the flesh." So what does it have to do with? The "appeal of a good conscience to God."
Second, a comparison is being drawn between the flood and baptism. Everyone who was touched by the flood died. The water never touched Noah and his family. They were saved in the ark, which is a type of Christ. We, likewise, are saved in Christ Jesus. He is our ark. "Baptism now saves you...through the resurrection of Jesus Christ."
Third, baptism is a means to salvation through faith. It is one of many graces in connection with salvation. This should be the understanding of "the washing of regeneration" (Titus 3:5). But baptism in and of itself does not save us. I think this is where all the confusion is coming from. Once again, you have people on two ends of the pendulum: those who argue that baptism absolutely saves us and grants us regeneration and eternal life, and those who argue that baptism does absolutely nothing as it is only "an outward sign of an inward expression." Both these groups are wrong.
When Lutherans, Presbyterians, and Reformed talk about baptism saving you, you have those who essentially believe like the Catholics, that it absolutely saves us and grants us regeneration and eternal life, but you also have those who understand it according to point number three. Everything is tied together through faith. Each one of these graces by themselves do not save us. But all of them together, with our faith, do save us; but not apart from Christ Jesus.
If what Lutherans, Presbyterians, and Reformed mean when they talk about baptism saving you is what I said in point three, then I agree with them. If they mean that water baptism itself has saving power, then I completely disagree with them, as does Scripture. "If you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved" (Rom. 10:9). I will now let the ESV Study Bible and ESV Reformation Study Bible speak:
ESV Study Bible
3:21 A comparison is drawn between salvation in the ark and baptism. In both instances, believers are saved through the waters of judgment, since baptism portrays salvation through judgment. The mere mechanical act of baptism does not save, for Peter explicitly says, "not as a removal of dirt from the body," meaning that the passing of water over the body does not cleanse anyone. Baptism saves you because it represents inward faith, as evidence by one's appeal to God for the forgiveness of one's sins (for a good conscience). Furthermore, baptism "saves" only insofar as it is grounded in the death an resurrection of Jesus Christ. Baptism is a visual representation of the fact that Christians are clothed with Christ (cf. Gal. 3:27), and in union with Christ they share his victory over sin.ESV Reformation Study Bible
3:21 Baptism, which corresponds to this, now saves you. Baptism is a sign and seal of God's grace in Jesus Christ. The startling statement that baptism "saves you" shows the closeness of the relationship between the sign and the reality it signifies. Noah's physical salvation through the waters of the flood prefigured the waters of baptism and the salvation they signify. Baptism symbolizes judgment on sin in the death of Christ and then also renewal of life. The floodwaters were a judgment on the wicked, and at the same time physical salvation for Noah and his family.not as a removal of dirt from the body. Lest his readers mistakenly attribute a magical or mechanical power to the sacrament, Peter states that the means of salvation is not performance of the external rite, but what it symbolizes—union with Christ in His death and resurrection.