The Chasam Sofer says the reason for nitel nacht is that the christians who were extremely anti-semitic used to get very violent with Jews on Dec. 25 or Jan. 7, depending on where they lived. Therefore they made a takana no one can go to beis medrash and learn because the streets are dangerous.
R’ Elyashiv says that the reason is that on Dec. 25, all the christians go to pray and there is so much tumah in the world, that al pi kabala if kedushas hatorah comes it can be extremely harmful. He says that this no longer applies nowadays in eretz yisroel since they are mostly, if not all arabs, and don’t have such a thing as christmas. So there isn’t that koach hatumah in Eretz Yisroel. Lefi his reasoning, this probably no longer applies in America either because it is highly doubtful that people go to church. It is not really a religious holiday anymore, but is a day that goyim get together, get drunk, scream rarara, and have a good time. It is much more probable to find them in the bar than at church. The reason for this is when the christaians wanted to make a new religion, they went to Rome and tried to convince people about chrisianity. Since there were such a variety of religions in Rome and were millions of names of gods in their books, no one cared to switch over to crissianity. The pagans, however, said they do not mind switching to crissianity as long as they don’t give up their fun and exciting day- Dec. 25. The crissians answered no problem, by us we’ll also celebrate Dec. 25. This makes sense also because their bible says he was born in the spring( i think) so why would they celebrate in the middle of the winter. Also, this thing with the man in the red suite climbing down chimeneys is only a few hundred years old, so it is not so much a religious holiday.
I assume that the reason that litvaks don’t keep nitel is because either they didn’t live in dangerous areas or because the reason I just mentioned. I heard b’sheim the chofetz chaim that he said he’ll take the “aveiro” of anyone that learns on nitel nacht. I don’t know the mekor for this though.