Why does wave-particle duality exist?
According to string theory the wave particle duality exists because electrons are actually standing waves, so electrons can act as waves.
There is good empirical evidence that electrons act as waves much as light acts as waves. Light in turn can act like a particle. The distinction between particles ( matter) and energy is blurred by the observed behavior of both electrons ( particles) and light ( waves) )
String theory takes these observations and using mathematical formulations proposes that particles are actually standing waves.
Standing waves can act as particles as the energy of the waves is localized. Standing waves can also act as waves as standing waves are waves.