John's narrative seems to be harkening back to an episode in chapter 7, whether the people say:

Could the authorities have realized that he is the Messiah? 27 But we know where he is from. When the Messiah comes, no one will know where he is from.” 28 So Jesus cried out in the temple area as he was teaching and said, “You know me and also know where I am from. Yet I did not come on my own, but the one who sent me, whom you do not know, is true.

John's is the prototypical "high theology" in which Jesus' parentage and place of birth are irrelevant. This gospel does not even mention his birth, and his home town is only named in the famous question "can anything good come out of Nazareth?" In chapter 7 Jesus refutes those who point out his lowly origins by emphasizes that he comes from God not from any particular town. His response to Pilate is along the same lines: after refusing to answer the question about his earthly origins, Jesus says: “You would have no power over me if it had not been given to you from above.”

The Book of Hebrews (7:3) displays a similar attitude when it compares Melchizedek and Christ:

Without father, mother, or ancestry, without beginning of days or end of life, thus made to resemble the Son of God, he remains a priest forever.

Conclusion: Jesus declines to answer Pilate about his is place of origin, because the author of this particular Gospel wants us to know that this information is irrelevant. Jesus comes from heaven - from God.

John's narrative seems to harken back to an episode in chapter 7, where the people say:

Could the authorities have realized that he is the Messiah? 27 But we know where he is from. When the Messiah comes, no one will know where he is from.” 28 So Jesus cried out in the temple area as he was teaching and said, “You know me and also know where I am from. Yet I did not come on my own, but the one who sent me, whom you do not know, is true.

John's is the prototypical "high theology" in which Jesus' parentage and place of birth are irrelevant. This gospel does not tell us anything about his birth, but instead begins with his eternal existence as the Word. (John 1) It then skips to John the Baptist's testimony about Jesus. His home town is named only to frame the famous question "can anything good come out of Nazareth?" (John 1:46)

In chapter 7 Jesus refutes those who point out his lowly origins by emphasizing that he comes from God, rather than being associated with any particular town or region. His response to Pilate is along the same lines: after refusing to answer the question about his earthly origins, Jesus says: “You would have no power over me if it had not been given to you from above.”

The Book of Hebrews (7:3) displays a similar attitude when it compares Melchizedek and Christ:

Without father, mother, or ancestry, without beginning of days or end of life, thus made to resemble the Son of God, he remains a priest forever.

Conclusion: Jesus declines to answer Pilate about his place of origin, because in this particular Gospel this information is irrelevant. Jesus comes from heaven - from God. Those who seek information about his birthplace are missing the point.