Hofstadter talks about such paradoxes in his book -- from what I remember, the paradox stems from self-reference (he also uses the example of "adjectives that describe themselves", aka the Grelling–Nelson paradox)
Self-reference breaks a lot of things, including our arrogance if it's done right
Could you explain how self-reference breaks our arrogance?
If someone were able to properly see themselves and evaluate themselves they are going to be much less likely to be arrogant as they will also consider their flaws