Why are dolphins so smart? It seems that dolphins have (among?) the highest encephalization quotients found outside of humans, higher even than chimpanzees. By the "use it or lose it" principle this indicates that intelligence must be particularly valuable in their niche. Why is that? They are predatory and social, and both of those are associated with intelligence, but why are dolphins smarter than other predatory pack animals? For example, is there something about being an air-breathing organism living in water that makes having a high EQ particularly adaptive?

It's less about the brain size, I think, more about the metabolic cost of brains. Brains are among the most costly organs to keep what it comes to oxygen demand. Air-breathing increases available oxygen for the body, hence mammals have larger brains that for example fish.

In diving animals the metabolic cost of brains is connected to the diving time (can't find the reference at the moment). Sperm whales shut down parts of their brains on long dives and do not have particularly active brains in general. Dolphins are mostly shallow diving animals. Maybe the selection favors higher brain metabolism potentially increasing the ability to catch prey and avoid predators? Pure speculation, though.