A reason I heard when I was younger (I do not have a mekor, so don’t bother asking for one) was that the minhag came about due to the chiefly Catholic practise of midnight Mass (a Christian prayer). Seeing as the Christians would get up at midnight to pray, it would create a kitrug against the Yidden for not going to the same lengths. Therefore, it was deemed better not to learn at all and not create an unflattering comparison.
If you accept this reason, then it makes sense to say that if you learn at all, you should learn the whole night. And that’s exactly what I intended to do, right up until the point I had to call the police after a fat man in a red suit broke my electric fireplace.