Bicycle design is a good example of where this matters: steel has a significant fatigue limit, and can endure cyclic stresses below that limit indefinitely. Aluminum has no fatigue limit, so any flexing is inevitably eating away at fatigue life. Thus aluminum bike frames have to be made much stronger and stiffer than otherwise necessary, to avoid bikes breaking unexpectedly due to fatigue. And that in turn means that aluminum bike frames don't have as much of a weight advantage over steel as you'd expect.
