Why do stars become red giants?

Answer: Hydrogen fusion moves to a shell around the core

Gravity compresses them more and more — Wrong. Red giants expand, not compress. When core hydrogen is exhausted, the core contracts and heats up, but the outer layers expand dramatically.

Hydrogen fusion moves to a shell around the core ✓ — Correct! When stars exhaust core hydrogen fuel, fusion stops. The core contracts and heats up under gravity. This heats the surrounding hydrogen shell, which begins fusing. Energy output increases, pushing outer layers outward—the star expands 100-1000x! The surface cools (red color, ~3000-4000K). Our sun will become a red giant in ~5 billion years, potentially engulfing inner planets!

Their temperature rises steadily as they age — Wrong. Red giants are actually cooler (hence red) despite expanding. The core heats up, but the outer layers cool as the star expands enormously.