Chad discussed this confusion in one of his videos.
Basically he said that, in physiology, when you think of catobolism, it is breaking down of some large substrate into smaller units, but because MORE BONDS ARE THEN MADE THAN ARE BROKEN it is an exothermic reaction/gives off energy.
Exergonic means more bonds are made than are broken (overall - energy given off) and Endergonic is more bonds are broken than are made (overall - more energy needed by system).