expressing a low opinion of something; expressing disrespect for something
He was shocked to learn that this so-called friend of his regularly made derogatory comments about him in his absence.
de (away)#rogare (to ask, question, propose) (Latin)
de rogue -- you always will have a low opinion of rogues (diseases, rouges is a Hindi word) de-erogat-ory = He is Arrogant. so everyone has a low opinion about him