Analyze each option to determine the correct animal classification.

• A. Bat - birds: Bats are mammals, not birds. They are the only mammals capable of true flight.
• B. Whale - mammal: Whales are mammals. They are warm-blooded, breathe air, give birth to live young, and nurse them with milk.
• C. Dolphin - fish: Dolphins are mammals, not fish. Like whales, they are marine mammals.
• D. Frog - reptile: Frogs are amphibians, not reptiles. Amphibians typically have moist skin and undergo metamorphosis.

Based on the analysis, the pairing "Whale - mammal" is correct.

The correct option is B.
$\boxed{\text{B. Whale - mammal}}$