Fact you say? Whoever wrote John's Gospel wasn't even there, nor does he claim he was. You are just assuming that Jesus was whispering in "John's " ear as was he was writing.
The Gospel of John is, as we have it, is heavily interpolated (i.e. edited) by someone else and does not always appear in order or even a logical sequence. Even as early as circa AD 250, Dionysius, bishop of Alexandria, argued that —based on the vocabulary, thought and style—the Gospel of John had two authors.
The fact is that the Nicodemus' reply makes no sense. Appeals to a translational error John made, as a way of rationalizing this problem away, makes even less sense when one remembers that "John" was writing under "inspiration" and therefore free or error (another presumption), and that therefore he could not have mistranslated.
Jesus' reply in John 3:5 only confirms that he meant from above (i.e. from heaven) and not again: "unless one born of the water and the spirit he cannot enter into he kingdom of God" which is saying somewhat different from John 3:3, but in either case Jesus never says one must be born again.
The other problem, besides Nic's off the wall response, is that the term "kingdom of God" in Judaism means simply Israel! Christians changed this to mean something else. So, as a Jew to a Jew, assuming this conversation ever took place, Jesus was telling Nicodemus that one must be born from above, that is from the water the spirit if he is to enter Israel! Clearly none of this makes any sense if we assume he was talking to Nicodemus in any language.
The differences between John and the Synoptics are brought to light with closer study, especially of relevant social science factors. John's historicity cannot be questioned on the basis of any such differences.
And your argument for this is a link which indicates that the definition/description for Israel contains the words God and Kingdom? Yeah that does fit your typical logical argument. But let me give you a hint, your conclusion is a non sequitur. Secondly you have never even acknowledged that Peter uses "ἀναγεννάω" BORN AGAIN.
I would reply that you in turn are assuming that whoever wrote John's Gospel was not there observing the conversation. Assuming that he was not based on nothing more than the absence of an explicit claim to the contrary amounts to an argument from silence.
It was at night, but the assumption that Jesus and Nic were the only two present may not be correct:
...The Method Of Teaching in these schools may be easily collected from the Gospels and Acts. The Doctors or Teachers generally sat. Thus our Lord sat down previously to delivering his sermon on the mount (Matt. v. 1.); as Gamaliel also did in his school. (Acts xxii. 3.)
Sometimes, however, the Jewish teachers, like the Greek philosophers, were accustomed to have their disciples around them, wherever they went, and to discourse, as occasion arose, on things either human or divine. In this way our Lord delivered some of his most interesting instructions to his apostles. Allusions to this practice occur in Matt. iv. 20. x. 38. xvi. 24. Mark i. 18. xvi. 24.
An introduction to the critical study and knowledge of the Holy Scriptures. , Volume 2
Thomas Hartwell Horne
Cordially,
If any Jew ever thought the word "Israel" meant the kingdom of God, he must have missed where God first used that name. It was recorded in Genesis 32:37-28:
And he said unto him, What is thy name? And he said, Jacob. And he said, Thy name shall be called no more Jacob, but Israel: for as a prince hast thou power with God and with men, and hast prevailed.
The word Israel has always meant Prince of God. As far as assuming Jesus told Nicodemus that he must be born of the Spirit to enter Israel is what makes no sense.