Functionally, this CB can only be used on your rivals. It’s always available as long as you don’t have a truce with them. This makes it an accessible way to quickly wage war on your rivals. There are three resources you can gain from this CB:
+2 monthly splendor in the Age of Discovery +100 to all three mana +30 power projection
For Meeting the Age Objective
“Humiliate Rival” is an objective of the Age of Discovery. Fulfilling it gives you +2 monthly splendor, which you use to purchase age abilities. However, the “Humiliate” peace term isn’t restricted to the “Humiliate Rival” CB. As long as you’re at war with your rival, you can humiliate them for 40% war score. If you’re playing a nation with strong early game abilities (like Portugal), you should find and humiliate a rival ASAP.
For Farming Mana
The CB has an exclusive peace term called “Show Strength”. This costs 100% war score but gives you 100 mana in each category. This is extremely useful in the early game — when mana is scarce and rivals are aplenty. Depending on who you’re playing as, you may be able to rival a weak nation that you can quickly conquer. Farm them for mana before the power gap between you grows and nullifies your rivalry. Over the course of the game, this method loses its appeal as you get stronger rivals. Your eligible rivals are limited to those who’re of equal strength to you. As you become more powerful, your group of rivals will also be larger than your previous ones. They’ll be harder to beat. You’ll eventually reach a point where the costs of winning far outweigh the benefits of farming mana.
For Weakening Your Rivals
This is where the CB shines. Since you can always use it on your rivals (except during truces), you can harass them anytime you see an opportunity. For example, if you see your rival struggling in a distant war, you can “help” their enemies by declaring a humiliation war. The “Humiliate” peace term also gives you +30 power projection while your rival loses -30 power projection.