The premise was that the earth was about to be destroyed, and some alien race could only save one species. Much to the chagrin of the humans, they saved the most intelligent species which turned out to be dolphins. It's not The Hitchhiker's Guide to the Galaxy, which is everybody's first suggestion. It's not Rescue Party by Arthur Clarke, either.
Could it be one of John Varley's Eight Worlds stories? Aliens almost destroy humanity because they recognize dolphins and whales as intelligent but humans as vermin.
Described at length in The Ophiuchi Hotline, the Invaders are inhabitants of gas-giant planets like Jupiter. They transcend the limits of four-dimensional spacetime and can manipulate time and space at will. They classify living beings in one of three categories: those such as themselves, who arise in gas giant planets everywhere, cetaceans such as dolphins and whales, and vermin, the last category including all sentient beings other than Invaders and cetaceans.
The Invasion of Earth was carried out to protect cetaceans from the effects of human civilization. Although no humans were directly killed, billions died as the Invaders dismantled all the infrastructure needed to support human civilization on Earth. The human population remaining on Earth after the Invasion is about the same as in prehistory, living in tribes without access to technology. This is a scenario that has been played out for millions of years across the galaxy. Inevitably the human species will be forced out of the Solar System altogether, to live between the stars where other displaced intelligences are already in residence.