According to the Jehovah's Witnesses, why was Jesus likely not born in December because of Levite temple service schedule?

This is about a particular reason why it was not likely for Jesus to have been born in December, based on an explanation I remember hearing from a Jehovah's Witness over a decade ago. I know that multiple arguments can be provided against a December birth date but this particular one is of interest mainly because I forgot the exact reasoning behind it and have not been able to find it explained anywhere. From what I remember of it, it had to do with the Levite temple service schedule and possibly John the Baptizer's father serving at the temple. If there is a reasoning along these lines, what was the explanation for it?