Bias that we have no bias
The observation that I see things clearly as they really are and you are biased.
The mind has evolved for us to keep our beliefs consistent. Science is one of the few methods we have to force us to confront and test our beliefs, but it need not be a threat to us to recognise that we have our weaknesses.
Bias that we are better than average
For example, we all tend to think that we are better drivers than average, have a better sense of humour than average etc. Evidently this can't be true globally, but it is good for us that we think of ourselves in this positive way.
Yes! We all do this - even wise people like you and me!
This is why it is so difficult of us to accept information that attacks these central views of ourselves. For example, if you have a strong belief that you have 'met the risen Jesus' your whole view of life will conspire to confirm your belief, even though you have no evidence to confirm that what you believe is really true. When I say evidence, of course I mean objective evidence that everyone else can share, not the evidence of coincidence and anecdote that we can all provide from our experiences.
In fact there is now a very strong body of opinion that memory is much less reliable than we like to think - however good we think our memory is. In fact, memory is generally wrong to a certain extent, but we have to accept that it is the best that we can do. Reading your own old diaries you probably don't remember what it was like to be that person, but your mind will build a narrative to minimise the cognitive dissonance around that disturbing observation.
We (as in 'we' who have taken the time to read and listen about the science of the mind, even if not study it professionally) know that our memories are shaped to be consonant with our current views of ourselves and the stories that we tell to explain ourselves. There is overwhelming evidence to suggest that our memories are not as reliable as we think they are, and no good quality evidence to the contrary.
How and what we remember affect our cognitive dissonance. Many think that memory is like a recorder, but now we know that it is a constantly constructed process. Your memories emphasise your current views over the top of the things that happened. Researchers have followed people's memories over time and it is found that our memories very much depend on whatever supports our current beliefs. We want to avoid being in a state of dissonance.
We should hold on to our beliefs but we should hold them lightly enough that we can accept new information, new ways of doing things and new improvements. It is harder to do this if it is something that you have invested a lot of effort into a particular point of view.
However, I assure you that it is perfectly possible to deconvert from a belief system and feel much happier about it.
Then again . . . I'm biased.