First I apologize if my question is trivial and for my poor English. I was wondering why my teacher states that "electron's wave-particle duality is verified if we observe diffraction of the electron flux when fired at a crystal" I mean, if the diffraction was considered to be only shown by waves, then why did the Davisson-Germer experiment lead to think that electrons behave like wave at specific scales ? My point is: what is the reason that makes the duality (applied to all particles) the more correct approach over considering that diffraction could be 'performed' by specific particles (in this case the electron) under specific conditions ?
Divisson Germer experiment proved that electron behaves as wave, since diffraction was caused by waves; its a property associated with wave.
But then, long ago when electron was discovered by J.J. Thompson. He found it as a particle in cathode ray tube.
So, Because of validity of both of these experiments, we led to the conclusion that electron behaves as particle as well as wave, under appropriate conditions.
See the image below, well its for photons but applies to electron as well,
Your question gets to the heart of the roles of experiment and theory in physics. If there hadn't been a complete theory already when the Davidson Germer experiment was performed, it would have been reasonable to conclude that electrons only behaved as waves in one experiment under special circumstances. But experiment is never the sole source of data about the world, you also need a theoretical framework to fit it in.
The real reason people believed in wave particle duality is because of the theoretical work of Einstein Bohr DeBroglie Heisenberg and Schroedinger. The theoretical motivation for matter waves was that they explained the old quantum condition in way consistent with Einstein's photon/light-wave duality. There was no experimental data used in discovering quantum mechanics, other than the blackbody law and the Ballmet spectrum. The rest was deduced from adiabatic invariance and the correspondence principle, culminating in Heisenberg and Schroedinger completing the Bohr and Einstein program for quantum mechanics respectively.
Davidson Germer in fact was a puzzle, because the wavelength of the electrons was not the one predicted by deBroglie. This was resolved by Hans Bethe, who introduced the concept of an effective mass for electrons in a metal, in a founding paper of condensed matter physics.