The Patronus requires a memory because it summons forward potential

Most defensive magic in the series draws on fear, anger, or willpower—emotions of the present moment. The Patronus stands alone in requiring something remembered, something already experienced and finished. The instruction isn't to feel happy now, but to recall when you were. This suggests the charm doesn't run on current emotion but on demonstrated capacity. The memory proves you survived to remember it, that darkness didn't win before, and the silver shape emerges as that proof made visible.

This explains why the spell fails under the hooded creatures' influence. They don't just create fear; they drain the possibility of happiness, making even memories feel false or unreachable. Without access to proof that joy existed, the charm has no foundation. The corporeal form might represent how specific the proof must be—not just 'I was happy once' but 'I was happy in exactly this way,' detailed enough to project forward as a shield.

The text repeatedly describes the memory as something the caster must feel, suggesting it powers the spell through present emotion, not abstract proof. The silver mist appears when students manage to feel the happiness again, not merely recall it intellectually. If memory served only as evidence, the creatures' despair-effect wouldn't matter—the past would remain factually true regardless of current feeling.