It is a difference in the underlying Greek manuscripts. The KJV use the Textus Receptus (TR) which includes the "I". The ESV uses NA27 which does not include the "I".
The KJV and NKJV include the "I" while the following do not include the "I": RSV, NRSV, ESV, NASB, NIV, TNIV, NEB, REB, NJB, NABRE, NLT, HCSB, CEB, GNT, GW, WKNT and NET.
Comfort says:
The variant is the result of a scribe making the text more suitable for public reading, for the insertion of με helps the reader immediately realize that Jesus was asking for self-identification as the “Son of Man.”
Philip W. Comfort, New Testament Text and Translation Commentary, Accordance electronic ed. (Wheaton: Tyndale House Publishers, 2008), 47.
Metzger says:
Both the variety of positions of με in the witnesses that include it and the fact that in the parallel passages the word is firm indicate that it was originally absent from Matthew’s account.
Bruce M. Metzger, A Textual Commentary on the Greek New Testament, 2d, Accordance electronic ed. (New York: United Bible Societies, 1994), 34.
Newman says:
It should be noted that the Marcan parallel (8.27) has “Who do men say that I am?” In addition some early Greek manuscripts of Matthew 16.13 also have “say that I am,” which indicates that there was some attempt in the early church to make explicit who was meant by this term. Moreover, when the question is repeated in verse 15, a shift is made to the first person (“I”). Nevertheless, as we point out at 8.20, it is generally advisable to retain the ambiguity of Matthew with “Son of Man” or “the One called Son of Man.” Only if retaining the third person in this verse would make the question addressed to the disciples in verse 15 seem odd, should translators say “I, who am the Son of Man.”
Further, it is important that readers not think that Jesus was asking which person was the Son of Man. It is not as if people were asking “Is Barabbas the Son of Man?” or “Is Herod the Son of Man?” or anything like that. Rather, Jesus is asking who people think the one who is called the Son of Man (namely, himself) really is.
Barclay M. Newman and Philip C. Stine, A Translator’s Handbook on the Gospel of Matthew, UBS Translator’s Handbooks; Accordance electronic ed. (New York: United Bible Societies, 1988), paragraph 4508.
