All reasoned enquiry is skeptical, including historical method, which Ehrman uses. Carrier puts me to sleep in a page and a half, so I've read little of him.
Well, historical method rules the supernatural out for a start. Otherwise all the gods, miracles, spirits, naiads, sprites, goblins, witches, warlocks, demons, Rainbow Serpents, all the gods and supernatural beings of history would be entitled to equal time. We have not a single authenticated example of a miracle, for example.
That's true, they were. So, of course were a great many other ancient documents. Note that these aren't treated differently ─ each ancient document must be assessed for what, where, when, who and why; and all historical conclusions, like all conclusions in physics, are tentative, subject to things we haven't found yet, or haven't seen the relationship yet.
That they made stuff up is obvious on the face of the record. Apart from the miracles and appearances, and temptation and so on, for example,
the author of Matthew requires Mary to have been a virgin because the LXX in translating Isaiah 7:14 renders Hebrew 'almah, young woman, as parthenos, virgin;
He invents the unhistoric 'Taxation Census' story to get Jesus to be born in Bethlehem to “fulfill” Micah 5:2.
He invents the unhistoric 'Massacre of the Innocents' story to get Jesus into Egypt to “fulfill” Hosea 11.1.
He absurdly sits Jesus across a foal and a donkey to ride into Jerusalem "to fulfill prophecy" (Matthew 21:2-5) in Zechariah 9.9;
And since the authors of Mark, Luke and John do the same or similar things, you notice that it would be possible to write the entire bio of Jesus in this way.
Oh, and apart from the fact that an authentic resurrection is a contradiction in terms, and that we have no contemporary, no independent, no eyewitness account of it, the accounts of the resurrection in Paul, the four gospels and Acts 1 each contradict the other five in major ways. The evidence is of stunningly low quality. You may remember the Ganesha milk-drinking miracles a few years ago, with videos on the net of statues of Ganesha "drinking milk". That evidence of a miracle was many orders of magnitude better in quality than the bible accounts of the resurrection, but no one who wasn't already a believer was persuaded by it.
To be clear, my own view is that there may have been an historical Jesus, but if there was ─ it's possible there was not ─ then we know very little about him, and the gospels are not innately credible or reliable sources and require considerable care.