Light must be quantum because it interacts with single atoms and either has an effect or does not have an effect. It has to do that in a single place. It is established that this is because of the quantum nature of light and not the quantum nature of atoms. But to create a two-slit interference pattern it must pass through both slits at once, so it has to be in two places. It must be a wave, and be everywhere. Feynman resolved the paradox. Light is a particle and is in exactly one place at a time. But it has a probability function that travels like a wave, that decides the probability that the photon is in each place. So a photon is a particle that appears in every possible way to travel exactly like a wave, except when it interacts with matter and acts like a particle.