Thanks for sharing this. I have to say, I wasn't particularly impressed with Carrier's use of evidence. A few examples from his initial argument are below.
Early on in his first 20 minutes he makes use of Ehrman's argument from How Jesus Became God to show there were cultural devices and types in the occupied Palestine Jewish communities that were applied to Jesus. Ehrman makes the case these were applied to him after his death while Carrier claims there is evidence in the epistles that support viewing this as the source of the Jesus myth in total such that no actual Jesus existed. His references (at around 33:45) include arguing Paul describes Jesus was an angel (described as an archetype in his presentation) as stated by Paul in Galatian 4:14. But what it actually says is, Galatians 4:14 - and even though my illness was a trial to you, you did not treat me with contempt or scorn. Instead, you welcomed me as if I were an angel of God, as if I were Christ Jesus himself. That seems like a forced reading of the verse to see it as saying Paul thought of Jesus as an angel rather than as providing an escalating comparison for how they received Paul.
Carrier notes that Paul contrasts Jesus with Adam who was created by God rather than born, failing to acknowledge that the text is making a literary comparison between the two (For if the many died by the trespass of the one man, how much more did God’s grace and the gift that came by the grace of the one man, Jesus Christ, overflow to the many!). Instead, Carrier claims this shows that as Adam was "manufactured" by God, so was Jesus. That also seems to be a forced interpretation of what is actually being said by Paul.
Around minute 38 he behaves as if he is ignorant of the diversity of Christianity's that were in competition in the 2nd and 3rd Centuries CE, which with the rise of teaching such as in Gnosticism are the cause for the sources of this time warning against those who would teach against Jesus being a living person.
He notes that Paul in Galatians tells us that he did receive of a gospel from man, but from Jesus through revelation which is not in dispute, but also assumes the point that when Paul tells people after Jesus' death that the only way they can receive the gospel is by revelation that this somehow applies to those who might have been around when Jesus was alive. James Jesus' brother or Peter who are known to Paul aren't included and it's unclear why Carrier would choose to apply this logic to everyone given the context of the epistles are to evangelized gentiles who would not have been able to know Jesus in the flesh.
He uses the claims of Paul that both Paul and the churches he establishes have received revelations as being evidence against the authenticity of a historical person we know as Jesus of Nazareth. But that seems to be unrelated like the above: it doesn't say anything about the time period or people who would be witnesses of a historical Jesus of Nazareth.
His argument around minute 42 that the description in Romans of baptism making all brothers and sisters to Christ the firstborn, thus explaining the apparent reference to James as Jesus' brother as referring to his baptism is one that Price made. But that breaks with some general rules of textual criticism. Common use of language implies that if Paul makes use of this phrase to refer to something other than kinship, we ought to see it in his writing as evidence of his authorship. Carrier doesn't do much to make this case by showing this is a device of Paul's, which makes sense because it isn't a device of Paul's. It's how he distinguishes James the brother of the Lord from other people.
The follow up point that the idea Jesus was born of David or of a woman (Romans 1:3 - regarding his Son, who as to his earthly life was a descendant of David; Galatians 4:4 - But when the set time had fully come, God sent his Son, born of a woman, born under the law) he claims Paul is speaking in allegory in Galatians 4. But fails to provide a relevant verse though he may mean v. 24 where Paul is specifically referring to his comparision to the wives of Abraham and children of a bond v. free woman. If so, that's problematic.
He also refers to Paul's use of "ginomai" as significant to show that Paul did not view Jesus as being born because he does not use "gennoa". But he doesn't take on the responsibility of explaining this well, since it is consistent of Paul's description of God having sent Jesus for a purpose. The problem Carrier sees here isn't clearly a problem, in my opinion.
http://biblehub.com/greek/1096.htm
I guess I still don't see what the point of the mythicicst argument really is given that we aren't limited to either "No Jesus" or "Resurrected Jesus the Christ, the Son of God". I see no reason to overlook his rather Mormon mopologetic-like use of scripture and history to no longer view the historical Jesus as a person who lived at one time, served as the catalyst for an explosion of beliefs and stories that have undergone centuries of countless cycles of expansion and synthesis, and whose actual biography would probably be almost completely new to all of us if we were able to have access to it.
So, that leaves me with this question: If the historical view allows for the mythologizing of a historical Jesus from a lost biography into his deified, ahistorical mythology why is there a need to completely remove Jesus from history? Especially in the way Carrier does above playing with facts which really puts me off?
ETA: I come at this with considerations that are somewhat extreme as well, though. I don't completely discount the views of Robert Eisenman who argues that the Roman Catholic church did much to write out Jesus' family from the narratives but that they can be found still; that Paul may have intentionally corrupted Christian teachings with some allegiance to Rome given his citizenship that defanged the teachings of this one branch of many rebellious Jewish sects into something more compatible with Roman rule; and that James was the theological heir to Jesus rather than Peter or Paul making the entire idea of priesthood authority as claimed by Mormonism central to what Mormon's call the apostasy. But he's a sloppy writer and loose in his thinking as well so he should be viewed with a lot of skepticism. I mostly retain some of his views among my own because they are hard to shake as speaking directly against Mormon views of the early and still authentically led Church of Christ before the apostasy.