They believed what they wrote. A writer biased in favour of their subject produces a better work than the so-called unbiased writer. The unbiased writer is boring, since they have no interest in what they write. The New Testament writers do not hide their bias, they declare unashamedly to totally support the events they record. This is in their favour.
Undisclosed bias is a most dangerous thing.
Much of our reporting in the daily papers and the electronic media contains undisclosed bias. The stories are simple and straightforward. The weakness of the disciples. We know that Matthew and Luke copy the work of Mark and yet they don't puff-up the story. We know that the gospels were written from about 50AD onward.