Convictions are more dangerous enemies of truth than lies.
-from Nietzsche's Human, all too Human, s.483, R.J. Hollingdale transl.
To me, this means that if one is so convinced of their "truth" (rather "beliefs") they will never take the time to try to find the truth. Or bother to ask themselves if their "beliefs" really are the truth.
I see this as a warning to those who see in absolutes. That if we believe with complete certainty what we have learned without investigating it and thinking it out completely, we become closed to the option that it could be wrong.
And this is dangerous to humankind as those that are too certain of their "righteousness" will spread those thoughts in a self-assured way.