What is the leading explanation for why male humpback whales sing complex songs?

Answer: Their songs communicate with other whales in a reproductive context

Their songs stun small fish so the whales can catch them — Humpback songs are not established prey-stunning weapons. Whales can make other sounds during feeding, but the elaborate repeated song is studied as a social and reproductive display.

Their songs communicate with other whales in a reproductive context ✓ — Male humpback song is thought to be a reproductive display heard by other whales. Researchers still debate its precise role, including how it affects other males and females. Communication is the broad explanation, not a proven single-purpose mating signal.

Their songs let them keep breathing while they are underwater — Singing does not let a whale breathe underwater. Humpbacks breathe air at the surface; producing a song while submerged does not extract oxygen from seawater.