Name for cognitive bias suggesting a person is special or important

Solution 1:

Falsely inferring a pattern where none exists is known as a type 1 error in statistics.

In this case the subject is under a delusion of self-reference, attributing undue importance to self in the events around him i.e. centered in (on) oneself, which is self-centring.

The general term for this cognitive bias - of seeing patterns in random events or data - is apophenia (apo - away [hence not true] phainein- to show). So I guess your subject might be under a self-centring apophenia, or in other words guilty of self-centring type 1 error.There might me a more specific term for it but I can't think of any.

Solution 2:

self-importance : 'Excessively high regard for one's own importance or station; conceit'

• an Anglo-Saxon synonym for: 'self-centred, vain, selfish, narcissistic, self-absorbed, egotistical, inward looking, self-important, self-obsessed, self-seeking, egoistic, egoistical'

and possibly also:

presumptuous : 'characterized by presumption or tending to presume; bold; forward'

Solution 3:

What you're describing is a person who thinks of himself/herself as exceptional in the original sense of the word - in different situations (s)he might think of himself/herself as being better than others, worse than others, or different in a way that invalidates any comparison. These days "exceptional" is often used to mean "better than", but the original meaning survives in phrases like "American exceptionalism" or "European exceptionalism" (in this case, the term might be something like "self-exceptionalism").

As far as an actual scientific term, you seem to be looking for an umbrella term covering several psychological terms for more specific biases, including:

Confirmation bias - The tendency to accept evidence that supports what we already believe and discard evidence that would force us to change our thinking.

Self-serving bias - The tendency to believe that our successes come from our own attributes, while our failures are the result of external factors beyond our control.