Nothing raises the hackles of Christians more than the suggestion the Jesus might not have actually existed. It is likely to provoke an emotional response containing elements of dismissiveness, categorical rejection, derisiveness, or mocking and ridicule. (What's that, you say? Christians use mockery and ridicule? Perish the thought.) That's what we see in an article called Does Richard Carrier Exist? by apologist Glenn Peoples, for example. OK, I know that it is intended to be humorous (and I agree his use of Bayesian inference is funny), but still it openly mocks the scholarly work of Richard Carrier, and includes ad hominem attacks that don't seem humorous at all, rather than presenting any reasoned argument against what Carrier says. And this is coming from a guy who has this to say about his own approach to argumentation:
Although I am a Christian (something that will become obvious to regular readers and listeners), when it comes to the sorts of debates that Christians and non-Christians get into, while I am a participant and a commentator, I do not want to be a cheerleader. Fairness is one of the most important measures of integrity, and I certainly do not wish to give religion a “free pass.” I criticise the arguments of Christians as directly as I do the arguments of non-believers when I think that they go wrong, as I think that by doing so I am actually doing the Christian community a service. Christians – like atheists – are not helped by having their intellectual standards lowered by poor argumentation that is accepted because of a partisan spirit. The pursuit of excellence involves the willingness to reject bad arguments even when they are given in defence of “your side.” Peoples
When it comes to the subject of mythicism, it's hard to find any arguments made by Christians that are free of the bias that is inherent in their religious ideology. After all, if you think it might even be possible that Jesus didn't exist, then you aren't a faithful Christian - by definition. The very idea is fundamentally incompatible with your ideology. So we should expect to hear plenty of pablum like this article from Peoples, or the "Why should we believe in Alexander the Great?" argument that is equally lacking in substance, but seems to be popular among Christians.
But ideology doesn't preclude a Christian from making a serious attempt to argue his point without belittling the proponents of mythicism. A more serious argument was made by apologist Trent Horn in Strange Notions. That's not to say that his argument lacks Christian bias, but at least he refrains from attacking or ridiculing those who take the idea of mythicism seriously. He makes four main points, which are ordered from what he considers to be the weakest to the strongest. And I'll address them in that order.
4. It is the mainstream position in academia.
Horn says "there is no serious debate among the vast majority of scholars in the fields related to the question of the existence of Jesus." And that might be true, if the vast majority of scholars consists of Christians, all of whom necessarily believe that Jesus existed. But that might be the reason he considers this to be the weakest of his points. That seems to be why he mentions only two scholars in support of this point, and both of them are atheists. But it is worth noting that atheist scholars who think Jesus existed don't share the level of absolute certainty that most Christian scholars have. For them, it's a matter of probability, which may be only a notch or two above the fifty percent level, while the mythicist may assess his confidence as a few notches below. And make no mistake about it. There are serious historians and scholars who are not highly confident that Jesus existed, because the evidence does not support that level of confidence. One thing is certain: the issue is not as cut-and-dry as Christians would have us believe.
3. Jesus’ existence is confirmed by extra-Biblical sources.
Horn uses three examples of this: two mentions of Jesus made by Josephus, and one made by Tacitus. One of those mentions by Josephus is widely regarded by scholars as a forgery. And while Horn states that it is mythicists who hold this opinion, there is no denying that even many Christian scholars agree that the passage in question was probably added to the writing of Josephus by Christian copyists. Even if we can't be certain of this, it casts serious doubt on its usefulness as an independent external reference to Jesus. The other two are more generally regarded as genuine words of the authors Josephus and Tacitus. And in that regard, I would agree that they serve as evidence. But I still think they are weak evidence at best. Both of them mention Jesus only in passing. These historical documents do not directly discuss the man or his works, as if the events surrounding the life of Jesus were not important enough to merit such discussion. And they certainly do not mention any of the miraculous events that surely would have been seen as noteworthy by any historian. Furthermore, both of these histories were written decades after the fact, when Christianity was fairly widespread. So the name of Jesus was probably well known at the time, and an occasional oblique mention of it in historical accounts doesn't seem surprising. Jesus was said to be the brother of James, so when Josephus mentions James, he identifies him as the brother of Jesus merely to distinguish him from others who have the same name.
2. The Early Church Fathers don’t describe the mythicist heresy.
This is an interesting argument. Horn says that the existence of mythicism in the early days of Christianity would have been met with considerable argumentation and resistance by the early church leaders that would be evident to this day. And while he may be right about that, it kind of misses the point. He's assuming that this mythicism would have been a heretical element within the faith. But as I have already discussed, Christians are not mythicists by definition (though some may have believed that Jesus was a spiritual being). The early church leaders assumed that Jesus existed, but that doesn't mean that non-Christians at the time made the same assumption. One could easily make the case that the gospels themselves were arguments for the existence of Jesus, designed by early church leaders to convince those who didn't believe. (Would we call non-believers mythicists?) But of course, the gospels today are not considered to be reliable historical documents.
1. St. Paul knew the disciples of Jesus.
Horn calls this "first-hand testimony", but that's not what first-hand testimony is. That's hearsay. Paul never met the live Jesus. If anything, he only knows what he has been told about Jesus by others. The fact remains that the entire bible doesn't contain one single word of eye-witness testimony to the life of Jesus. This is something that many Christians can't seem to grasp. They insist that the New Testament does contain eye-witness testimony, but in fact it only tells about people who are said to be witnesses. It never presents their words directly. And aside from those biblical accounts, there is no independent account of any of those events they supposedly witnessed.
In the final analysis, I don't find Horn's argument to be convincing, but I appreciate his attitude. I'd be perfectly willing to concede that Jesus existed if I could find some convincing reason to think that it's true. But I can't find any reliable factual information that would lead that conclusion. It doesn't matter to me, one way or the other. If there was a Jesus, or if there wasn't, it doesn't rock my world. I think there's a good chance that there was some person that the legends were based on. But that person almost certainly was not the legendary figure Christians see as their savior, who was born of a virgin in Bethlehem, performed many miracles, and rose from the dead. If there was an actual Jesus, he probably wouldn't be recognized by Christians as the man they worship.