While not a FE, it would be for a similar reason to why we can see the sun during the day and why we see different stars at night throughout the year. They aren't synchronized.
What do you mean by "they aren't synchronized"?
The sun takes roughly 24 hours to circle above Earth, the stars take roughly 23 hours 56 minutes so over the course of a year it would make 1 more cycle than the sun.
The moon is even slower and makes roughly 12 or so fewer cycles each year. (if I did the math right).
The moon isn't always opposite the sun.
During a full moon the moon is opposite the sun and is visible at night.
Close to a new moon, the moon is close to the sun and is visible during the day.
This applies for both RE and FE.
Edit: corrected that the moon is slower, not faster.