In what way are the photoelectric effect and the double-slit experiment in conflict

The photoelectric effect suggests that light is a stream of particles,
whereas the double-slit demonstration suggests that light is a stream
of waves. 

The conflict arises when you try to hold onto the idea that it must be
either one or the other, and it can't be both. 

Once you make peace with the concept that on the sub-atomic level,
a phenomenon can possess the properties of both waves and particles,
the conflict evaporates, and you can once again sleep peacefully at night.