What Causes the Nonuniform Changes in Lunar Illumination?

Question:
Hi! Could you help with the following question regarding the moon’s illumination?
From the US Naval Observatory: “Although Full Moon occurs each month at a specific date and time, the Moon’s disk may appear to be full for several nights in a row if it is clear. This is because the percentage of the Moon’s disk that appears illuminated changes very slowly around the time of Full Moon (also around New Moon, but the Moon is not visible at all then). The Moon may appear 100% illuminated only on the night closest to the time of exact Full Moon, but on the night before and night after will appear 97-99% illuminated.”
Why? I was unable to find any explanation of this phenomenon, only documentation of its existence. The moon goes from 2 and 3% increases near full and new phase to 10 and 11% near first and third quarter. Since the time between each primary moon phase is still around 7 days, the apparent acceleration of the moon’s orbit near quarter phases is perplexing.
Thanks for your time!
Answer:
I believe that this description is referring to the effect of observer parallax on the apparent phase of the Moon. This parallax effect is small, but is most apparent near New and Full Moon.