[sculptor]

Why indeed red giants? Perhaps this is really the place to start. The usual argument seems to go that when the inner core runs out of hydrogen, but there is still hydrogen in a shell just outside the core, then the core starts to collapse gravitationally. When it is smaller, same mass but smaller radius means it produces a hugely greater gravitational "compression" of the hydrogen layer just above it, thereby causing enormously higher fusion rates in the shell just above it, thereby heating up the atmosphere, thereby fluffing up to a red giant.

But same problem: why is the gravitational collapse UNSTABLE? I can see that a partial answer is that gravitational collapse on its own does not produce enough local heating per unit reduction in radius to increase the pressure enough to prevent further collapse, whereas if there is hydrogen present, there is enough heating per unit reduction in radius to increase the pressure enough to prevent collapse, hence stable.

Am I even right this far?

But even if this explains why a hydrogen-fusing core is stable but a hydrogen depleted core is unstable, it doesn't explain why the next shell out, where there IS hydrogen fusion going on, doesn't fluff up to the point where the fusion rate drops back to normal. So, even if cores without hydrogen are unstable and collapse, why red giants?