Who are the protagonist and antagonist of this story?
In addition to both of the fine answers above, I would also argue that two of the social forces Tthakker speaks of as antagonists are poverty and youth. The name of the couple is a tip-off here: Young. These two protagonists love each other very much, but have not yet learned to communicate well. Furthermore, their immaturity and inexperience also leaves them vulnerable to manipulative people like Madame Sofronie.
Poverty is also working against the pair. They want to share their love for one another in the traditional way at Christmas time, with gifts. I don't think it is so much about their own materialism, but society's emphasis on demonstrating love during this holiday with gifts, thus spoiling the "true meaning" of Christmas. The sacrifices each made for the other will ultimately be what the pair can hold on to. Combs go out of fashion, gold watches lose their luster. Love, however, is the real gift Jim and Delia can give.
Delia and James are the protagonists in the story. They sacrifice the only items of value they have in order to buy the perfect Christmas gift for each other. The antagonist is Madame Sofronie. She runs the store where she sells wigs and other items for the hair. She is an uncaring woman who represents the coldness of the outside world that serves as a contradiction to the warm, loving relationship that James and Delia share.