As I've heard it the reason for not learning Torah on nittle nacht it to avoid supporting the forces of evil which are more prevalent(?) at that time. I am wondering why those Jews don't avoid learning Torah before every non-Jewish holiday?
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There are other reasons for not learning on Nittel besides "supporting forces of evil" including the reason given by the Taamei MinHagim that the Christians would become impassioned on their holiday, and would go out and kill Jews therefore would need to stand guard instead of learning Torah (Ta'amei Ha-Minhagim p. 500).
If you are wondering if that is the reason then why celebrate it at all then you are in good company with the Belzer Rebbe OB"M who held that there is no reason to hold nittel anymore other than for the reason of "minhag avosainu".