Why were AA cruisers vulnerable to submarines?

Why did so many anti-aircraft cruisers still fall to submarine attack?

Their air-defence role offered no immunity to torpedoes, and a relatively small cruiser could be sunk by fewer well-placed hits.

A ship's air-defence role did not stop enemy submarines from attacking it. Submarine losses therefore do not by themselves measure the effectiveness of its anti-aircraft weapons. Smaller cruisers could be sunk by relatively few torpedo hits. Where a torpedo struck could be decisive.