When you derogate someone, you belittle them or put them down. If you tend to derogate everyone around you, it's unlikely you'll win the election for class president.
It's extremely common in politics to hear a candidate derogate their opponent, or for one political party to derogate another. When they do this, they are focusing on their adversary's weaknesses and faults in an attempt to harm their reputation. This sense of weakening someone's reputation dates from the 15th century, and it stems from the Latin derogare, "take away," a root derogate shares with derogatory.