Which high priest said it was better for one man to die for the people than for the whole nation to perish?

Answer: Caiaphas

Caiaphas, high priest that year, said this; John explains he was unknowingly prophesying that Jesus would die for the nation.

“But one of them, named Caiaphas, who was high priest that year, said to them, “You know nothing at all!”— John 11:49 (BSB)