John Calvin's Commentary on the Gospel of John 3:
verse 5- 6
Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.
"Chrysostom, with whom the greater part of expounders agree, makes the word Water refer to baptism. The meaning would then be, that by baptism we enter into the kingdom of God, because in baptism we are regenerated by the Spirit of God. Hence arose the belief of the absolute necessity of baptism, in order to the hope of eternal life. But though we were to admit that Christ here speaks of baptism, yet we ought not to press his words so closely as to imagine that he confines salvation to the outward sign; but, on the contrary, he connects the Water with the Spirit, because under that visible symbol he attests and seals that newness of life which God alone produces in us by his Spirit. It is true that, by neglecting baptism, we are excluded from salvation; and in this sense I acknowledge that it is necessary; but it is absurd to speak of the hope of salvation as confined to the sign. So far as relates to this passage, I cannot bring myself to believe that Christ speaks of baptism; for it would have been inappropriate.
"We must always keep in remembrance the design of Christ, which we have already explained; namely, that he intended to exhort Nicodemus to newness of life, because he was not capable of receiving the Gospel, until he began to be a new man. It is, therefore, a simple statement, that we must be born again, in order that we may be the children of God, and that the Holy Spirit is the Author of this second birth. For while Nicodemus was dreaming of the regeneration (palingenesia) or transmigration taught by Pythagoras, who imagined that souls, after the death of their bodies, passed into other bodies,  Christ, in order to cure him of this error, added, by way of explanation, that it is not in a natural way that men are born a second time, and that it is not necessary for them to be clothed with a new body, but that they are born when they are renewed in mind and heart by the grace of the Spirit.
"Accordingly, he employed the words Spirit and water to mean the same thing, and this ought not to be regarded as a harsh or forced interpretation; for it is a frequent and common way of speaking in Scripture, when the Spirit is mentioned, to add the word Water or Fire, expressing his power. We sometimes meet with the statement, that it is Christ who baptizeth with the Holy Ghost and with fire, (Matthew 3:11; Luke 3:16,) where fire means nothing different from the Spirit, but only shows what is his efficacy in us. As to the word water being placed first, it is of little consequence; or rather, this mode of speaking flows more naturally than the other, because the metaphor is followed by a plain and direct statement, as if Christ had said that no man is a son of God until he has been renewed by water, and that this water is the Spirit who cleanseth us anew and who, by spreading his energy over us, imparts to us the rigor of the heavenly life, though by nature we are utterly dry. And most properly does Christ, in order to reprove Nicodemus for his ignorance, employ a form of expression which is common in Scripture; for Nicodemus ought at length to have acknowledged, that what Christ had said was taken from the ordinary doctrine of the Prophets.
"By water, therefore, is meant nothing more than the inward purification and invigoration which is produced by the Holy Spirit. Besides, it is not unusual to employ the word and instead of that is, when the latter clause is intended to explain the former. And the view which I have taken is supported by what follows; for when Christ immediately proceeds to assign the reason why we must be born again, without mentioning the water, he shows that the newness of life which he requires is produced by the Spirit alone; whence it follows, that water must not be separated from the Spirit.
"6. That which is born of the flesh. By reasoning from contraries, he argues that the kingdom of God is shut against us, unless an entrance be opened to us by a new birth, (palingenesia ) For he takes for granted, that we cannot enter into the kingdom of God unless we are spiritual. But we bring nothing from the womb but a carnal nature. Therefore it follows, that we are naturally banished from the kingdom of God, and, having been deprived of the heavenly life, remain under the yoke of death. Besides, when Christ argues here, that men must be born again, because they are only flesh, he undoubtedly comprehends all mankind under the term flesh. By the flesh, therefore, is meant in this place not the body, but the soul also, and consequently every part of it. When the Popish divines restrict the word to that part which they call sensual, they do so in utter ignorance of its meaning;  for Christ must in that case have used an inconclusive argument, that we need a second birth, because part of us is corrupt. But if the flesh is contrasted with the Spirit, as a corrupt thing is contrasted with what is uncorrupted, a crooked thing with what is straight, a polluted thing with what is holy, a contaminated thing with what is pure, we may readily conclude that the whole nature of man is condemned by a single word. Christ therefore declares that our understanding and reason is corrupted, because it is carnal, and that all the affections of the heart are wicked and reprobate, because they too are carnal.
"But here it may be objected, that since the soul is not begotten by human generation, we are not born of the flesh, as to the chief part of our nature. This led many persons to imagine that not only our bodies, but our souls also, descend to us from our parents; for they thought it absurd that original sin, which has its peculiar habitation in the soul, should be conveyed from one man to all his posterity, unless all our souls proceeded from his soul as their source. And certainly, at first sight, the words of Christ appear to convey the idea, that we are flesh, because we are born of flesh. I answer, so far as relates to the words of Christ, they mean nothing else than that we are all carnal when we are born; and that as we come into this world mortal men, our nature relishes nothing but what is flesh. He simply distinguishes here between nature and the supernatural gift; for the corruption of all mankind in the person of Adam alone did not proceed from generation, but from the appointment of God, who in one man had adorned us all, and who has in him also deprived us of his gifts. Instead of saying, therefore, that each of us draws vice and corruption from his parents, it would be more correct to say that we are all alike corrupted in Adam alone, because immediately after his revolt God took away from human nature what He had bestowed upon it.
"Here another question arises; for it is certain that in this degenerate and corrupted nature some remnant of the gifts of God still lingers; and hence it follows that we are not in every respect corrupted. The reply is easy. The gifts which God hath left to us since the fall, if they are judged by themselves, are indeed worthy of praise; but as the contagion of wickedness is spread through every part, there will be found in us nothing that is pure and free from every defilement. That we naturally possess some knowledge of God, that some distinction between good and evil is engraven on our conscience, that our faculties are sufficient for the maintenance of the present life, that -- in short -- we are in so many ways superior to the brute beasts, that is excellent in itself, so far as it proceeds from God; but in us all these things are completely polluted, in the same manner as the wine which has been wholly infected and corrupted by the offensive taste of the vessel loses the pleasantness of its good flavor, and acquires a bitter and pernicious taste. For such knowledge of God as now remains in men is nothing else than a frightful source of idolatry and of all superstitions; the judgment exercised in choosing and distinguishing things is partly blind and foolish, partly imperfect and confused; all the industry that we possess flows into vanity and trifles; and the will itself, with furious impetuosity, rushes headlong to what is evil. Thus in the whole of our nature there remains not a drop of uprightness. Hence it is evident that we must be formed by the second birth, that we may be fitted for the kingdom of God; and the meaning of Christ's words is, that as a man is born only carnal from the womb of his mother; he must be formed anew by the Spirit, that he may begin to be spiritual.
"The word Spirit is used here in two senses, namely, for grace, and the effect of grace. For in the first place, Christ informs us that the Spirit of God is the only Author of a pure and upright nature, and afterwards he states, that we are spiritual, because we have been renewed by his power."