Hugh McLeod of Gavingvoid captures it well.
David McRaney writes on the same thing in his book (You are now less dumb - 2012).
Once something is added to your collection of beliefs, you protect it from harm. You do this instinctively and unconsciously when confronted with attitude-inconsistent information.
Just as confirmation bias shields you when you actively seek information, the backfire effect defends you when the information seeks you, when it blindsides you.
Coming or going, you stick to your beliefs instead of questioning them. When someone tries to correct you, tries to dilute your misconceptions, it backfires and strengthens those misconceptions instead.
Over time, the backfire effect makes you less skeptical of those things that allow you to continue seeing your beliefs and attitudes as true and proper.
I think these two insights capture the essence of why it is so difficult to get people to change their minds. Because accepting YOUR idea often means abandoning one of their own.