At one point, Dr Carrier said:
That Matthew is deliberately contradicting Mark because he is arguing against Mark is vastly more probable than that Matthew and Mark are correctly describing exactly the same events.
I've got to ask "Why is it more probable that Matthew deliberately contradicts Mark?" Carrier accuses Christians of the mistake
...in fundamentalist “harmonizations” of Gospel contradictions: they think they have “rebutted” the conclusion that the Gospels are contradicting each other if they can think of “any” possible way to harmonize the accounts, developing a fanciful “just so” story that makes everything fit, by assuming a hundred things not in evidence. But that ignores the fact that that account is actually extremely improbable.
Yet Carrier does the exactly this if he can't explain why Matthew deliberately contradicting Mark is more plausible than other Christian interpretations. Biases can go both ways. Read the whole interview at the following link.
Debunking Christianity: An Interview With Richard Carrier About His Book, "Proving History"