A similar puzzle presents itself after John the Baptist's arrest. Matthew says, "when Jesus heard... he withdrew into Galilee." Mark says, "After John had been taken... Jesus came into Galilee." Luke, having already previewed John's arrest before Jesus' baptism, leaves it unconnected from his "Jesus returned to Galilee". But John says, "when the Lord knew that the Pharisees had heard that Jesus was making and baptizing more disciples than John... he left Judea and went away again into Galilee." (The Fourth Gospel does not record the Baptizer's arrest, but he drops from the narrative a good while before the quotation above.)
These four accounts each touch on a pivotal phase near the outset of Jesus' ministry, and - if they can be looked at in tandem - may portray a similar situation to the Pharisees' threat of Luke 13.
In Luke 13, the puzzle is odd enough. Why would Jesus leave Judea because Herod Antipas wanted him? The Tetrarch of Galilee had no jurisdiction in Judea. But, as Luke 23 illustrates, the Judean arrest of a Galilean can be offered in extradition to Antipas. On that occasion, we're told, Herod turned down Pilate's offer. And it's most likely that Antipas' hunt (from Luke 9) had been suspended the moment Jesus entered Judea. Why borrow back trouble already cast off?
But whether or not Luke and Luke's Pharisees knew what Antipas might do, the point at hand is established. That these Pharisees acted as if Jesus might leave Judea, because of Antipas, shows that there must have been customs of extradition between Judea and Herod's Tetrarchy.
It all seems clear enough on the balance. But how does our knowing about extradition customs affect how we might view that early phase of Jesus' ministry, which was mentioned above?
Matthew says it was news of John's arrest that drove Jesus into Galilee. The fourth Gospel says it was knowledge that some Pharisees were marking Jesus down as a bigger political thorn in their side than even John had been. If these are not contradictions, they must be related somehow. But taken separately, each account has its problems.
The verb in Mt.4:12 ("went away") suggests not just that Jesus entered Galilee, but that he specifically needed to leave where he'd been, because of John's arrest. Surely Matthew would not have us believe that Jesus somehow risked angering Herodias, as John had (Mt.14:3-4). But surely the fourth Gospel would not have us suppose that the Pharisees could do much more than harass Jesus, as they had the Baptizer in Bethabara (Jn.1:24-28). Perhaps, west of the Jordan, the Pharisees could
Taken together, these accounts offer answers for one another. Viewed historically, the most effective way for the Pharisees to get rid of Jesus was extradition to Galilee. Any minor arrest could have served that purpose quite easily; at least, potentially. And if this was historically what the Pharisees were thinking, it could very well have been John's arrest that got them thinking about it. The comparison in John 4:1 also suggests this.
The scenario under consideration is that John's arrest prompted the Pharisees to wish Herod could take Jesus also. Or perhaps Jesus merely feared they would soon wish this. It makes no difference. Chronologically, either case would require that Jesus' knowledge in John 4:1 came extremely near the time of Jesus' hearing news in Matt.4:12. That is, approximately one right on top of the other, but not simultaneously.
Finally, what does this suggest for the origins of our sources, here?
What Mark offers as merely sequential ("after"), Matthew relates as explicitly causal ("when"). However, if Matthew himself had less than the full picture (of what's being suggested today), his vague sense of causality becomes more understandable. Perhaps knowing only that these two events were related in some way, Matthew simply summed up.
But much later on, for his part, the fourth Gospel writer gave more detail about the Pharisees' role in causing Jesus' withdrawal from Judea, after John had been taken by Herod. Of course, since the fourth Gospel writer had some other reason to avoid mentioning John's arrest and beheading, he could not explicitly clear up the matter of Matthew's confusion.
Like Luke-Acts, the Gospel of John is more careful than Mark or Matthew to avoid making specific indictments of Herodian rulers. But if these parts of their narratives do in fact coincide with the same early, pivotal phase of Jesus' historical ministry, then what John attributes to the jealousy of the Pharisees may actually refer to the same decision Matthew attributes to the Baptist's arrest.
It seems probable that Jesus left Judea over concerns that Herod's seizure of John could have given the Pharisees an idea to get rid of Jesus by extradition to Galilee. Did the Pharisees actually plan this? Perhaps not. But that part doesn't matter. That the Pharisees could have conceived such a plan seems like it must have been reason enough for Jesus to leave Judea.
A related question is how did Jesus go on to avoid Antipas' notice until John's death? But once Antipas did want Jesus gone from Galilee, at that moment, the tables turned and Judea became Jesus' safe place to be.