it's a strategic decision. if one civ is warmongering and getting denounced by the rest of the world, denouncing them yourself will make everyone else like you more. alternatively, if many civs are already friends with you and you denounce someone, you may make whoever you denounce a target for your friends to denounce as well. it's a method of controlling diplomacy
sometimes it will make no difference (except for the civ you are denouncing) and other times it can be a poor decision if the civ you are denouncing is friends with many others