Amoeba can use its body as a respiratory surface, why humans cant

Oxygen diffuses through cell membranes, regardless whether we’re talking about amoeba or mammalian cells.

The difference is in the fact that amoeba obtain their oxygen from the outside environment, which has a virtually infinite supply of oxygen and rapidly equilibriates to replenish the tiny amount of oxygen the amoeba depletes from the environment.

Mammalian cells on the other hand have to get their oxygen from blood because they do not have access to the outside environment. Blood has a finite amount of stored oxygen which must be replenished periodically. This is why we’ve evolved lungs.

Because we evolved lungs and don't breathe through our skin.