Bart Ehrman constantly plays up alleged discrepancies in the Gospels to disprove their historical reliability. This involves a "horizontal" reading of the Gospels. In honor of Holy Week, I will cite a striking example to illustrate how I approach the same issue:
And when the centurion, who stood facing him, saw that in this way he breathed his last, he said, “Truly this man was God's son” (Mk 15:39).
When the centurion and those who were with him, keeping watch over Jesus, saw the earthquake and what took place, they were filled with awe and said, “Truly this was God's son!” (Mt 27:54).
Now when the centurion saw what had taken place, he praised God, saying, “Surely this man was innocent!” (Lk 23:47).
i) In Matthew and Mark, the centurion calls Jesus "God's son". But in Luke, the centurion says Jesus was "innocent". How do we account for the difference? There are different possibilities. You could propose additive harmonization. Maybe the centurion made both statements. I think additive harmonization is sometimes the correct explanation, but I think that's clunky in this particular context.
Or you might say Luke relies on a different tradition of the crucifixion at this point. That's somewhat problematic for the detailed accuracy of the accounts.
Finally, you might say Luke's version reflects an editorial change. He redacted Mark at this juncture. I'm going to pursue that explanation.
ii) One objection some people might raise to that harmonization is that it makes Luke put words in the mouth of the centurion that he never said. But doesn't that involve taking unacceptable liberties with historical events?
Sometimes that's a valid criticism. If a writer puts a statement on the lips of a character who didn't actually say it, we usually think that detracts from the accuracy of the account. However, it depends.
Suppose a guy says he was "shooting the bull" with some friends. Suppose I repeat that conversation to an immigrant who lacks a command of idiomatic English. "Shooting the bull" would conjure up a completely misleading image in his mind. Does that mean the guy was on a hunting range? In that context, it would be perfectly appropriate for me, in recounting that conversation, to reword it. To use a different phrase. Although I'm quoting someone, yet in that situation I substitute a different phrase because the original idiom would be misleading to the foreign listener. It wouldn't mean to him what it meant to the original speaker.
iii) What does "son of God" mean in the Gospels? Occasionally it's used as a Davidic title (e.g. 2 Sam 7:14). But that's contextual. And you have many passages where it functions as a divine title rather than a Davidic title.
iv) A striking example is where demons recognize Christ's true identity (Mk 3:11, 5:7; Mt 8:29 & Lk 8:28). This is a bit hair-raising because human observers are overhearing a conversation between two inhuman agents. The demon is inhuman. And it senses something inhuman about Jesus.
That's not to deny the humanity of Christ. But what the demons detect has nothing to do with his human aspect or Davidic sonship. They discern something that's not empirical. That Jesus is, in a sense, God in disguise. The demons are naturally privy to something about Jesus that's inevident to human observers. Something that transcends the five senses. Demons were in a unique position to immediately apprehend his underlying identity.
v) Then we need to consider the connotation of that designation for a pagan. If Ares is the son of Zeus and Hera, that means he is the same kind of being as Zeus and Hera. If Zeus is a god, Hera is a goddess, and Ares is their son, then Ares is a god.
vi) Now, the Gospel writers don't think Jesus is "God's son" in a pagan sense. However, the Gospels were written in the lingua franca (Greek) of the Roman Empire. The Gentile mission was a major focus of evangelization in the NT church. Therefore, I think they trade on an overlapping sense. By that I mean, they are using "son of God" in an ontological sense. They use it to indicate that Jesus is the same kind of being as the Father. The phrase intentionally plays on that like father/like son implicature.
The main difference is a different conceptualization of God. Yahweh is a very different kind of divinity than Zeus. Hence, his son has no point of origin.
Unless the Gospel writers are using "God's son" ontologicaly, it would be extraordinarily misleading to make this a standard designation for Jesus, given so many Gentile readers–considering the default connotations of that title for Gentiles/pagans. Put another way, the Synoptics would need to take great precautions to guard against otherwise inevitable misunderstanding, given the associations that title would automatically have for non-Jewish readers. Yet they don't generally do that.
vii) There are, however, some further gradations. I think Mark's audience is fairly indiscriminate. Notable scholars (e.g. R. T. France, Martin Hengel, Robert Stein) think his immediate audience was the church of Rome. And that, of itself, was a federation of Gentile and Messianic Jewish house-churches.
By contrast, Matthew targets Jewish readers. That's a control on how the implied reader would assess the centurion's statement. A Jewish read would make allowance for the centurion's heathen background. And he'd distinguish that from Jewish theism.
However, Luke has a Gentile target audience. On the lips of a Roman soldier, that would have a pagan connotation, and Luke can't assume that his audience has the same standard of comparison as Matthew's. There is, moreover, evidence that Matthew and Luke occasionally redact Mark to forestall misimpressions.
So I suspect that Luke substituted a dynamic equivalent. Although "innocent" is not synonymous with "God's son," the centurion was vindicating Jesus by his exclamation ("Surely, this is God's son!"), so Luke's alternative faithfully conveys the speaker's intent.