Our writer's question comes from a close reading of the Lukan text. Most of the time, when people of the Church read the Bible, they don't read with eyes of wonder and anticipation, but with a sense of resignation-they already know the stories so they seldom discover things like our writer did. In this case, Luke 3.1-20 relays the story of John and his ministry and it's followed by Jesus' baptism in verse 21-22 and then his genealogy in 23-38. But when we read the whole passage with wondering eyes we discover this: "When John rebuked Herod the tetrarch because of Herodias, his brother's wife, and all the other evil things he had done, Herod added this to them all: He locked John up in prison. When the people were being baptized, Jesus was baptized too." The problem is, how could John be baptizing anyone while locked up in prison?
One has to agree with our writer that the passage in question is either out of chronological order or else John wasn't the one who baptized Jesus. This could pose a perplexing problem, since Luke specifically says he wrote his book so we could have "an orderly account" (Luke 1.3). However, both Matthew and Mark specifically say John baptized Jesus, and the gospel of John strongly implies it. How can we deal with the discrepancy?
Part of the problem with reading the Bible through our modern eyes is that we often read the Bible as though we reading a history book or a biography. But the four gospels are neither history, though they contain some historical records, nor are they biographies, even though some of the information is biographical.
Both histories and biographies are written with some general guidelines. Unless there is some specific literary reasoning, they are both written in chronological order. So, unless we're reading a flashback, we don't expect to read about John Glenn's trip on the Shuttle before we read of his senate career. The order of events in both biographies and histories begin at a set point in time and move along chronologically.
Not so for the gospels. The four gospel writers weren't writing as novelists nor historians. They wrote to convince an audience of the wonder and glory of Jesus. Matthew wrote for a Jewish audience. Luke wrote for non-Jews. And John specifically states th purpose of his gospel: "These are written that you may believe that Jesus is the Christ, the Son of God, and that believing you may have life in his name" (John 20.21). And so the writers were less concerned about chronology than in getting their point across.
For instance, when Jesus went into the temple and overturned the money changers' tables and ran the merchants out, John records the incident as if it were one of the first things Jesus did in his ministry (John 2). On the other hand, Matthew and Mark place the incident toward the end of his ministry (Matthew 21, Mark 11). In each case, the event is placed in its context to serve some purpose of the writer: to make a point, not to serve as a chronology of Jesus' work.
So, why does Luke record John's arrest before Jesus' baptism? One reason may be that Luke wrote it that way to keep John's story separate from Jesus' baptism story. Why would he want to do that? Because of the point Luke may have been making about Jesus' baptism and genealogy.
When Jesus was baptized, Luke writes, "When the people were being baptized, Jesus was baptized too. And as he was praying, heaven was opened and the Holy Spirit descended on him in bodily form like a dove. And a voice came from heaven: 'You are my Son, whom I love; with you I am well pleased'" (Luke 3.21-22) The very next verse begins "Now Jesus himself was about thirty years old when he began his ministry. He was the son, so it was thought, of Joseph, the son of Heli" (3.23). It seems apparent that Luke had one thing in mind as he wrote this passage: to show that Jesus was God's son as pronounced from heaven, not the product of a long and noble lineage. And the John the baptizer story would just have gotten in the way of Luke's literary device.
So, yes, John baptized Jesus. Luke doesn't preclude that, he just isn't terribly interested in that fact. Instead, Luke was willing to suspend chronology in order to make a point. He wanted to show that Jesus was God's son with "the certainty of things you've been taught" (Luke 1.4).