According to Wikipedia, "confirmation bias is a tendency to search for or interpret new information in a way that confirms one's preconceptions and to irrationally avoid information and interpretations which contradict prior beliefs." As with illusion-of-control bias, confirmation bias is not exactly unknown in the stock market.
Perhaps the reason for its prevalence is that much of the data we need is inconsistent. A person who diligently puts down a pro- and con- list, and assiduously searches for disconfirming information for his or her initial conclusions, might wind up doing nothing at all. There's no global weighting card that enables us to assign proper weights to this positive datum and that negative datum.
Instead, we have to use filters, diversification and a dollop of fatalism. Even the best filters don't screen out all lemons, and filtering is subject to an optimality criterion. Screening out potential lemons also means screening out some potential oranges. Since none of us know the future, we have to pick a screening system, an optimality point, and basically stick with both. And let the outliers go without beating ourselves over the head about missing them.
It's easy to see how this fatalism can transform into confirmation bias. When we're anxious and uncertain, a slice of reassurance can do us a lot of good. We all need reassurance from time to time, but reassurance junkies are also hooked on confirmation bias.
Perhaps it's like anchoring, in the sense that we investors can never completely shake free of it. If this be the case, then self-knowledge is the best way to cope. Sometimes, it hurts to say that such-and-such is outside of one's circle of competence...but saying so does indicate a certain emotional maturity.