Cognitive Dissonance.

It is entirely possible to hold two conflicting concepts in your head at the same time.  It isn't necessarily desirable to do so, but it is possible.

For instance let's take something conceptual.  There is wrong and then there is more wrong.  If I ask Little Lord Fonteroy what 2+2 is and his answer is 5, and Sweet Little Virginia Valentine's answer is 6,315, you know that they're both wrong, but one is more wrong.  There are degrees of "wrongness" and there are degrees of "rightness".

Sometimes it's easy to tell if an answer is wrong and how wrong it is.  2+2 is a good example of that.  The numbers are small and almost every person has dealt with the equation so often that they don't even need to calculate it.  Sometimes it's difficult to tell if an answer is wrong, but you can still tell that a particular answer is not only wrong but is obviously wrong.  An equation like 571*26 would be an example of that.  Most people don't have the skill to do this equation in their head and would have no idea what the answer is unless they use either a calculator or a pen and paper.  However, if you told someone that the answer was either 14846 or it was 1, just about anyone who has taken arithmetic could tell you that the first answer is not only much more likely to be true than the second but it's obvious that "1" is entirely incorrect.  You may not know if 14846 is absolutely correct but you do know that 1 is wrong and 14846 would be, at the very least, closer to the correct answer.

This is an important skill to have for us to have as it allows for some quick estimations to be performed.  It also demonstrates that we will attempt to evaluate the credibility of a statement using general principles that seem reliable enough.  This doesn't guarantee that we will come up with correct answers using this method but it has shown to be effective in most situations to give a quick assessment of something.

How does this apply to cognitive dissonance?

When followers of the Abrahamic religions read stories such as Noah's Ark they are faced with cognitive dissonance.  You don't have to be a zoologist to know that the concept that a boat could be built to house a breeding pair of all the land animals on Earth is obviously wrong.  You don't have to be a nutritionist to understand you could not then gather and store enough food on this boat to sustain a breeding pair of all the land animals on the Earth.  You don't have to be a management specialist to understand that eight people cannot care for what would amount to millions of animals (as well as themselves).  You may not know exactly how big an ark would have to be or how many people it would take, but you know that Noah would not have had the capability of building a ship that size, gathering the necessary food and storing it along with tending to everything for a year with no fresh water.  This answer is clearly more wrong.

The story of Noah's Ark is clearly impossible as written.

Some people will protest that their god used it's magic to make the whole thing work.  What kind of a retort is that?  Your god had the ability to just do away with all the "sinful" people and to miraculously raise their orphaned children without harming even one cell of any other living thing on this planet, but that's not the way the story tells it.

If you want to write in your own revisions to the story I welcome it.  You couldn't do any worse. That wouldn't change the original version, however, nor would it be any more plausible than stating that Houdini fed the animals and Penn and Teller made them fit on the ark.  Invoking miracles is NOT the same as an actual suspension of the physical makeup of the universe for a specific purpose that leaves no evidence of it ever having occurred nor any reason to believe it ever actually happened.

I may not know how a magic trick was done but I harbour no illusions that magicians have command of forces that actually allow them to walk through walls, saw people in half, read my thoughts or remove the physical mass of the Statue of Liberty from the universe without harming it and then restoring this same matter by force of will.  If you do have the belief that magicians have secret knowledge of the supernatural then you really should stop participating in any activity that involves a group (such as voting!) and perhaps you should secure some sort of legal proxy to tend to your affairs as well.

So, if you find yourself saddled with the state where you know that the story isn't true but you believe that it is, congratulations on a rather obvious cognitive dissonance.  One way or another it will be like the repair that you know needs to be done but continue to neglect.  You may be able to "get away" with it but you will always be in danger of a break down.