Beliefs are the mind's architectural features.  Together they create a landscape that forms the shape of your psyche.  Your individual schema will be tested by external information that you may either accept or reject. Will you keep on smoking even though you know it may lead to cancer? Will you buy things you don't need even though it's production contributes to the consumption of natural resources and fossil fuels? Will you accept culture even when it is selling you things for the sake of continual consumption?

Consider the processes at work within your head.  Remember when someone said something that you thought was completely ridiculous.  Perhaps they made a statement that referenced a stereotype and revealed a belief.  Perhaps they generalised someone based on their gender, ethnicity, colour, creed, political views.  Perhaps you challenged that belief then they became angry.  Perhaps they were upset and it was just too much for them to process.

That belief is their identity and, for some people, a threat to someone's identity is a same as a threat to their existence.  For others, who are adaptable and open-minded, this may not be a threat but an opportunity to update their beliefs. The process below demonstrates the cognitive process that occurs when new information is presented.

A problem of truths.  When someone is holding onto a belief and they base their understanding of the world on that belief there is a lot of resistance when they are confronted with contradicting information.  This often happens with opinions (which aren't facts).  The world is flat says one, there is a photo that shows the world as a spherical type object.  Or, God created the world in 7 days but there is evidence of a big bang that initiated the creation of our universe.  The line between opinion, truth and fact is often blurred but most often that is irrelevant.  What is more relevant is that if someone believes in something and has a strong emotional attachment to that belief (and it is therefore valuable to them) then they are almost certainly going to have a reaction to anything that challenges that belief.

The discomfort of dissonance is also down to the fact that an individual may acquire 2 contradictory beliefs.  They could be in 2 minds about something. This discomfort is something that the mind must reconcile and address to reduce the any stress caused by the contradiction. One of the stress reducing techniques that someone may use (either consciously or sub-consciously) is to reject the new information and return to the old belief.

There may be a number of reactions but often the coping mechanisms that people use are dependent on how they rationalise something to themselves.  Most often this rationalisation is self-serving and can stand to reinforce the original belief regardless of the new information available to the brain.