"My guess is the real underlying purpose is to discredit Josephus because he substantiates Jesus."
Well, he substantiates Jesus a little bit, in the sense that he certainly describes the man as having lived and been executed, and continuing to have followers, yes.
The part of Josephus that reads of Jesus "He was the Messiah" and states that he was raised "on the third day" is almost certainly a gloss added by the later Christian scribes who preserved the text.
How can we be pretty sure about that?
Two things, one less persuasive, and the other more persuasive.
The less persuasive thing is that ancient manuscripts of Josephus preserved in Arab lands don't contain the Messiah and resurrection references, but do contain the rest of the stuff about Jesus having been lived, taught, done some marvels, executed, and still having followers. The key bits about Jesus having been the Messiah and raised "On The Third Day" (without any explanation of what "The Third Day" means) aren't there. But one could easily argue that Muslim scribes deleted that stuff.
By far the most persuasive thing is Josephus himself. Josephus' Jewish Antiquities, in which the reference to Jesus and James and John the Baptist are included, is a MASSIVE work. Josephus himself was a priest of the Temple and had been a Jewish general in the Galilee fighting against the Romans in the revolt before his capture. He knew his Jewish history, and he knew all of the intimate rites of the Temple, and all of the legends and traditions of the Jews. And Josephus is extremely pedantic. He's well aware of being extremely well educated and brilliant, and he flaunts it. Every detail that he knows about everything, he gives...in extenso. When one considers that his Jewish Antiquities start with Adam and Eve, and give the priestly legends and midrash concerning the ENTIRETY of biblical history as well as contemporary history, one realizes just how pedantic and detail-oriented Josephus was. Lost in that sea of verbiage - it's an utterly massive work - is the reference to Jesus. There is simply no way at all, if Josephus ben Matthias, really thought that Jesus was THE MESSIAH, that he would give Jesus three sentences, and give Jesus' brother James about thrice the commentary. If Jesus were the Messiah, or even if Josephus believed he had been resurrected, we can only expect that Josephus would have gone on for pages and pages and pages, bleeding ink out of every pore, with every detail of the man's life...and the life of his parents, grandparents and great-grandparents all the way back to Adam and Eve. That's the way Josephus treats every OTHER major figure in his Jewish Antiquities.
It's just not POSSIBLE that this priest of the Temple and pedant extraordinaire would flippantly devote three sentences to a man he said was RESURRECTED AND THE MESSIAH! That's not how Josephus wrote ANYTHING, and to MERELY bury three sentences about the echatological denoument of Jewish belief, AND a resurrection miracle to boot? No. That's impossible. That's just not Josephus. I've read most of the stuff he wrote. It's interesting, because it is like a time capsule of what the Jewish priests of the Temple, before the Talmud and the rabinnical tradition was established, believed and did. It gives us all those details that we know about the inner workings of the First Century in the Middle East and before. It's because of Josephus that we know more, in greater detail, about practically every aspect of 1st Century Judaea than we do about any other spot on the planet in the First Century, including Rome proper. He was that comprehensive and that pedantic.
It's IMPOSSIBLE that had Jesus existed and started a cult, that he wouldn't appear in Josephus. And sure enough, Jesus DOES appear in Josephus. So we know that the man really did live, and really had a following and really was executed. He wasn't a legend. But Josephus being Josephus, we can also tell that the bit in our translations of Josephus about Jesus being "The Messiah" and being raised from the dead "on the third day" were not written by Josephus. Read him, and you know that there is absolutely, positively no way at all that he would have let pass THE MESSIAH and a RESURRECTION with anything less than about three chapters. One sentence? Not possible. Not for Josephus. Further, the bit about "On The Third Day" is cryptic. Josephus was writing for a Greek and Roman audience who knew little about Judaism and nothing whatever about Christianity. "On the Third Day" is a Christian prayer formula, from the Nicene Creed, which dates from about 220 years after Josephus wrote. Beyond that, just sitting there along "On The Third Day" is opaque. On the third day after WHAT? Josephus never writes like that. He would tell us the third day after the crucifixion, describe the crucifixion, the second day and the third day, tell us what the weather was like, and tell us who Pontius Pilate had for dinner each night (I am only slightly exaggerating).
I guess it's not really fair to anybody for me to write all this without giving the entire "Testimonium Flavianus", the whole "Testimony of Josephus" about Jesus.
First I'll give what Josephus says about Jesus in the texts we have. Then I'll give what he probably really did say about Jesus, based on Josephus' style in the rest of his thousands of pages of history, and based on what's in the Arabic manuscript:
From Jewish Antiquities, at 18:3:3
"Now there arose about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him many of the Jews and many of the Gentiles. He was the Messiah. And when Pilate, at the suggestion of the principal men among us, had condemned him to the cross, those that loved him at the first did not forsake him; for he appeared to them alive again on the third day, as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day."
What Josephus probably wrote:
"Now there arose about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him many of the Jews and many of the Gentiles. And when Pilate, at the suggestion of the principal men among us, had condemned him to the cross, those that loved him at the first did not forsake him. And the tribe of Christians, so named from him, are not extinct at this day."