A hologram can be recorded with a single beam,IF if the beam is spread out enough so that it illuminates both the object and the recording plate (and light scatters off the object onto the plate). However, that is completely equivalent to having separate object and reference beams.
Imagine what would happen if the object were just a tiny piece of a mirror, so it throws a narrow beam of light onto a spot on the plate. With no reference beam, the plate would be exposed at that spot and that's all there is to it. But with a reference beam added, that narrow beam of light from the object would interfere with the reference beam at that spot; and thereby a diffraction grating would be formed at the spot. Look up the principle of a diffraction grating, and you will be able to understand that the diffraction grating formed there is exactly what is needed to deflect (diffract) the reference beam into the direction in which the object light was traveling when the grating was formed. That is the fundamental principle of holography.
