Here's where the "explanation "lost" me.
The discussion went from "behaves like a wave" to it is a wave. Not buying it. If it can be both, there needs to me an explanation for that; analogous or otherwise...
LOOSELY: All matter consists of waves. Everything is quantized. Everything exists at a certain state/energy level. For very tiny things (electrons, protons, photons, etc.), the allowed energy levels are easily distinguished because these levels are clearly separated by energy zones that are forbidden (you can only stand on the run of a step in a staircase and not the rise). As we consider larger and larger objects, the permitted states run closer together (rise becomes smaller and smaller) to the point that they seem to run together into one smooth continuum of allowed states. This creates the illusion of no quantization for macroscopic objects, which is described by Newtonian Mechanics (which may be considered a subset of Quantum Mechanics).
Waves have wavelength and particles have mass. De Broglie related the two qualities in a simple equation. So, they are related and experiments using the relation do work!
It is neither a wave nor a particle; it is a photon. There are measurements that give "wave-like" results; when performing one of these, the photon has all the properties of a wave. There are other experiments that give "particle-like" resluts; when performing of these other expemints, the photon has all the prpoerties of a particle.
Photon is a photon is a photon. (If you prefer Rand to Stein, delete the first two words of the previous sentence.) Wave and particle are our descriptions of experimental results, not descriptions of photons.