We do go into the water. But, that's all we do. In fact, a handicapped person could be put into the water by someone else. Then someone else dips us into the water and brings us back up. We don't do any work at all. The reality is that any work done in baptism is done by God. We are not saved by our actions or those of the baptist, and we are not saved by the water. Just as circumcision (the sign of the old covenant) did not make anyone God's chosen people before Christ came. They were chosen because they would bring Jesus, but their salvation still required their obedience and faith.
God saved Noah and his family. God did it, Noah did not. But, Noah still had to obey God by building the ark and getting into it so he could be saved.
"Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father who is in heaven."
And Peter said unto them, "Repent ye, and be baptized every one of you in the name of Jesus Christ unto the remission of your sins; and ye shall receive the gift of the Holy Spirit."
As therefore ye received Christ Jesus the Lord, so walk in him, rooted and builded up in him, and established in your faith, even as ye were taught, abounding in thanksgiving. Take heed lest there shall be any one that maketh spoil of you through his philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ: for in him dwelleth all the fulness of the Godhead bodily, and in him ye are made full, who is the head of all principality and power: in whom ye were also circumcised with a circumcision not made with hands, in the putting off of the body of the flesh, in the circumcision of Christ; having been buried with him in baptism, wherein ye were also raised with him through faith in the working of God, who raised him from the dead. And you, being dead through your trespasses and the uncircumcision of your flesh, you, I say, did he make alive together with him, having forgiven us all our trespasses; having blotted out the bond written in ordinances that was against us, which was contrary to us: and he hath taken it out that way, nailing it to the cross; having despoiled the principalities and the powers, he made a show of them openly, triumphing over them in it.
We are justified by faith apart from the works of the law, not apart from works. If we could follow every law perfectly, we could be justified by our works. Since we cannot, God sent Jesus as our way to be justified. Jesus tells us us that to believe is a work. Religions denying any works go against what Jesus said.
They said therefore unto him, "What must we do, that we may work the works of God?" Jesus answered and said unto them, "This is the work of God, that ye believe on him whom he hath sent."
For by grace have ye been saved through faith; and that not of yourselves, it is the gift of God; not of works, that no man should glory. For we are his workmanship, created in Christ Jesus for good works, which God afore prepared that we should walk in them.
Where then is the glorying? It is excluded. By what manner of law? of works? Nay: but by a law of faith. We reckon therefore that a man is justified by faith apart from the works of the law.