Well, perhaps it refers to a behavior in a Christmas story where a character eats without restraint, just as pigs are known for eating voraciously. Maybe in the story, there's a big Christmas feast and someone is acting like a pig at the table, eating lots of food quickly and messily.
In the context of a Christmas story, 'eating like a pig' might be a descriptive phrase. Christmas is a time of feasting. So if someone is described as eating like a pig, it implies that they are indulging in the Christmas food without much regard for propriety. They might be gobbling up the turkey, stuffing, and all the delicious treats without taking the time to savor or be polite. It could also be a humorous way to show a character's love for Christmas food or their lack of self - control during the holiday feasting.