Quantum Behavior As Extreme Classical Behavior

[wotanub]

As it has already been said, you shouldn't try to derive quantum mechanics with classical intuition. Classical mechanics is quantum mechanics within a limit. In many cases it is straightforward to revive the results of classical mechanics from quantum mechanics.

You keep going to the basketball in a hoop example. The basketball is a wave, but consider its wavelength with respect to the distance it travels and the size of the hoop. Now consider the wavelength of an electron compared to Young's slits.