The Romans, from which we got the Julian calendar, used to use a 10 month calendar before hand. Why 10 months? It's because January through March was a time that nothing could be done. It was too cold, the crops couldn't be planted and it's why Aries is the first sign of the Zodiac. This was their new year starting in mid-March.
The months were: Martius for March, Aprilis for April, Maius for May and Iunius for June because the J didn't exist yet. Months July through December were simply numbered. Quintilis for July literally meaning "Fifth Month". Sextilis, September, October, November, December for August to December which was tenth month.
Later on when Julius added January and February the 7th through 10th months names remained instead of being renamed Undecember and Duodecmber as the 11th and 12th months. So If Jesus was born in October it kinda fits. He was born then as the shepherds would still have been out in the fields with their flocks and it's a misunderstanding of the naming of the months. Instead of being born in the 10th month which at that point as named "October" it was changed to the 12th month and put in "December".
Or maybe I'm just overthinking things and deserve some puzzle pieces.