The original meaning of this idiom was very different than it is today - and that could be a good thing! It is said that back in the day , the medieval one, hunters would go out with big sticks and hit the bushes while making loud noises. The purpose was to scare any birds or animals hiding in the bushes. In retrospect, was that really such a good idea?  I mean, depending on what kind of animal might be hiding in the bush - would you really want to startle it and have it possibly charge you?! Anyway... These days it means avoiding the topic at hand or the answer to the question.

In horse racing sometimes the jockeys beat the horses to go faster and that's where this phrase originates. A horse who is worn out can't go any faster no matter how much it gets beat. It is pointless. So to beat a dead horse means to bring up a topic that cannot be changed or concluded. ( source )