I do not know what reasons Bruno Bauer, Albert Schweitzer and George A. Wells had, but I think they maintained different points of view enough to not lump them all in the same boat. Maybe you like to tell us any of these reasons and we can discuss them here.
However, take care with your argument because it can turn against you. I can ask why Carrier and Doherty are unable to persuade the majority of historians and the answer will be similar or worse for mythicist side.
The argument, which you say can be turned against me, was to point out that all sceptic writers have known full well that Paul’s letter say’s “save James, the Lord’s brother”. But for numerous reasons, which we have discussed to death, and which almost all those authors have addressed directly, they do not accept that Paul is talking about anyone known to be an actual family member.
Are you denying that these authors have all long since known of those words in Paul’s letter?
This is strictly false. Some Pauline epistles, usually admitted as genuine, speak about the Jesus' family. Either true or not that the family of Jesus existed, what is clear is that some early texts of Christianity spoke of people who had known Jesus as a human. May be you wanted to say another thing and you were not too precise.
Albert Schweitzer:
“Jesus as a concrete historical personality remains a stranger to our time, but His spirit, which lies hidden in His words, is known in simplicity, and its influence is direct. Every saying contains in its own way the whole Jesus”. (Albert Schweitzer: The Quest of Historical Jesus, London, Adam and Charles Black, 1911; p. 399)
A strange "sceptic".
Which Pauline letters make credible claim to knowing anyone who was a family member of a living Jesus? Which of those letters even make any credible claim to anyone ever knowing or meeting a living Jesus?
Can you quote those letters saying those things, please.