Of course Jesus does not contradict himself and in regards to the word "water" in John 3:5, there are those who would argue that the natural sense of the passage parallels "water" with being born out of a mother’s womb (verse 4) and with "flesh" (verse 6). Simply stated in that case, Jesus told Nicodemus that in order to see the kingdom of God two births are necessary. The first is a physical, literal, "flesh" birth (which is, of course, accompanied by amniotic "water") and the second is Spirit.
There are also those who would argue that Jesus mentions "living water" in John 4:10, 14; 7:37-39 and in John 7:38-39, we read - "He who believes in Me, as the Scripture has said, out of his heart will flow rivers of living water. But this He spoke concerning the Spirit. The Holy Spirit is the source of living water and spiritual cleansing. If "water" is arbitrarily defined as baptism, then we could just as justifiably say, "Out of his heart will flow rivers of living baptism" in John 7:38. If this sounds ridiculous, it is no more so than the idea that water baptism is the source or the means of becoming born again.
Yet there are still others who would argue that "water" is used in the Bible as an emblem of the Word of God, and in such uses it is associated with cleansing or washing. (John 15:3; Ephesians 5:26) When we are born again, the Holy Spirit begets new life, Divine life, so that we are said to become "partakers of the divine nature" (2 Peter 1:4). The new birth is brought to pass through "incorruptible seed, by the Word of God, which lives and abides forever" (I Peter 1:23), but the Holy Spirit is the Agent who accomplishes the miracle of regeneration. *So to automatically read "baptism" into John 3:5 simply because it mentions "water" is unwarranted.*