why is adherence to one's pride dangerous?

King Creon imposes his will beyond that og the Gods' devine will.

In Antigone, Sophocles describes the type of pride that allows men to create laws that substitute for divine principles. In other words, when Creon creates a law because he believes it is divine will, that is the ultimate display of punishable pride, for no man can ever create a law that is equal to or above divine right.

Creon doesn't bend his will and, in the end, his stubborn pride costs him his family. I'm going to hook you up with GradeSaver site that deals exactly with your question in greater detail. Some of what I wrote is from there but you can find more if you wish.