What we have here is not just a bifurcation but actually a dichotomy.
The difference is that a bifurcation just suggests that something has forked into two ways but with a dichotomy the two ways are considered opposite or antithetical. A river splitting into two streams is a bifurcation while good and bad are a dichotomy.
This is one of the oldest and most appealed to dichotomies in scripture. It began in the making of man:
Gen 2:7 And the LORD God formed man of the dust of the ground, and
breathed into his nostrils the breath of life; and man became a living
Adam was not a three part being (body, soul, spirit) but rather a two part being (body/flesh/dirt and breath/spirit).
Breath and spirit are synonyms. In the original languages (Hebrew, Greek, Latin, German, Aramaic and even Olde English) there is no distinction).But not the breath you and I know which is just gases. To the ancients the breath was a mysterious, magical force. For example when Yehovah breathed his own breath into the clay status of himself it came alive and had all kinds of mental faculties. He became a living being (aka "soul").
I suggest to you that if you grasp the dichotomy you will be able to understand a great deal of scripture as you never have before. For example, Paul's writings:
Gal 5:16 ISV So I say, live by the Spirit, and you will never fulfill
the desires of the flesh. Gal 5:17 For what the flesh wants is
opposed to the Spirit, and what the Spirit wants is opposed to the
flesh. They are opposed to each other, and so you do not do what you
want to do. Gal 5:18 But if you are being led by the Spirit, you are
not under the Law. Gal 5:19 Now the actions of the flesh are
obvious: sexual immorality, impurity, promiscuity, Gal 5:20
idolatry, witchcraft, hatred, rivalry, jealously, outbursts of anger,
quarrels, conflicts, factions, Gal 5:21 envy, murder, drunkenness,
wild partying, and things like that. I am telling you now, as I have
told you in the past, that people who practice such things will not
inherit the kingdom of God. Gal 5:22 But the fruit of the Spirit is
love, joy, peace, patience, kindness, goodness, faithfulness, Gal
5:23 gentleness, and self-control. There is no law against such
things. Gal 5:24 Now those who belong to the Messiah Jesus have
crucified their flesh with its passions and desires. Gal 5:25 Since
we live by the Spirit, by the Spirit let us also be guided.
Now modern translators have replaced "flesh" with "carnal nature" and "breath" with "spirit" but it is the same old dichotomy and the terms "carnal nature" and "spirit" are really inappropriate and obscure the original dichotomy evident in the original languages. Here are some more examples:
Joh 6:63 ISV It is the Spirit [breath] who gives life; the flesh
accomplishes nothing. The words that I have spoken to you are spirit
[breath] and life.
Breath gave life to Adam's flesh. That's why Jesus can say that so confidently.
So back to John:
Joh 3:6 What is born of the flesh is flesh, and what is born of the
Spirit [breath] is spirit [breath]. Joh 3:7 Don't be astonished that
I told you, 'All of you must be born from above.' Joh 3:8 The wind
blows where it wants to. You hear its sound, but you don't know where
it comes from or where it is going. That's the way it is with everyone
who is born of the Spirit [breath]."
Note that Jesus/John ascribes volition to the wind: "...The wind blows where it wants to..."
The key to verses 6 and 7 is verse 8. That which originates from the flesh profits nothing and is at odds with that which is born from above, which gives life.
Part of this is intended as actual and part is metaphor.
The neuter verb is a participle. Participles have no gender of their own, they just have to agree if there is a noun to attach to.