Refusing to abandon an extreme position or attitude. When someone says this about you, they fail to see that your position is not only correct, but the only sane choice. When you say this of someone, they're completely blind to reality.
A good clue to your personal intransigent moments can be your feeling tempted to shout "La la la la la!" while you opponent is talking, so as to blot out the sound of their meaningless prattle.