electromagnetic radiation - Why call it a particle and not a wave pulse?

My physics textbook says that photoelectric emission provides conclusive evidence for the particle theory of light. Apparently, since photoelectric emission only works at certain frequencies, we can conclude the electrons do not build up the energy from the light and thus the light energy must not be reaching the electrons as a continuous wave but rather as discrete particles called photons. However, wouldn't energy build up also not occur if we considered light as wave pulses instead of particles? If so, why is it then that we insist it is a particle? Or is it a wave pulse but just called a particle? If it is, then why?