Without knowing a lot more detail of the state of the relationship between the parents it's impossible to judge.
One possible scenario is that there is little communication between the parents and the mother was worried about the repercussions of requesting any change to the standard 'week about' arrangement. She may have thought it in the child's best interest to leave things as they are rather than being selfish about it and demanding she have the child over Christmas.
As I say, just one possible scenario!
Keith raises a good point. After my parents' divorce, I really didn't want to have anything to do with my father. (He had been physically abusive to my mother, and to some extent, to me and my sister as well.) However, the court ordered me to have unsupervised visits with him, and my mother was afraid that if she didn't obey the court order, my father would get custody of me. (Her losing custody was a realistic possibility despite my father's behavior. My father was a former judge and politically powerful in our small town, and had managed to get my mother committed for a time to a mental hospital even though she wasn't insane.) So, I don't think it's fair to assume that the mother being away from her child on Christmas means she doesn't care about the child.
Also, I know that this is not the place for political debate, but I would like to comment on something I have noticed in this thread. Some of the posts here could be taken as implying that mothers have more responsibility to care for their children than fathers do. (I'm not sure if that was what the posters intended, or not.) I strongly feel that we as a society should hold
all parents, whether female or male, as responsible for the well-being of their children. Many children today are being raised by single mothers who really struggle to provide single-handedly for their children's needs (not only financial needs, but children's needs to be kept safe, to be fed, bathed, educated, and loved.) Raising a child is a huge job for one person to do alone. Unless fathers as well as mothers are seen as responsible for their children, our children won't get the care they need.