Intensity oscillations of the specular (0,0) RHEED spot during layer-by-layer growth are well known, whereas the associated oscillation of the position of the RHEED streaks remains more controversial. We revisit the problem of the origin of the peak-to-peak oscillations observed in RHEED spectra during layer-by-layer epitaxial growth. For this purpose we perform solid-on-solid KMC simulations to describe the growth, and we use the kinematical approximation to simulate RHEED intensity profiles. We show that the peak-to-peak oscillations result from the angular dispersion of the incident beam and the periodic oscillation of the size of the growing islands, without the need of invoking the strain relaxation in the islands.