Particle Wave duality shows us that waves and particles are the same thing. Therefore electrons can be viewed as both particles and waves. The wave properties of electrons can be seen in the double split experiment where a diffracted electron interacts with itself.
If a single electron was diffracted, what would happen to it's physical properties? How could the mass spread out like the wave? Similarly how would the charge and spin spread out? These properties are usually considered to be contained in particles, yet if a single electron was diffracted, it surely could not become many particles spreading out.
Also, what would happen if something interacted with this 'electron wave' causing part of it to act like a particle again? The wave can't be able to turn back into a particle after spreading out so much, yet it must still be able to act like a particle for certain interactions.