Why do some volcanic islands slowly grow and then sink over time?

Volcanic islands form when repeated eruptions pile up lava above sea level, creating new land. Over time, however, the oceanic crust beneath the island cools, becomes denser, and slowly sinks. At the same time, erosion from waves and weather wears the island down. This combination can turn a volcanic island into a chain of islands, seamounts, or even submerged guyots, as seen across the Hawaiian-Emperor chain.