The reason it's my pet peeve is because I use "begging the question" in its correct form all the time to describe an otherwise difficult concept. Once you put a name on something, it's much easier to understand and talk about. But when the name is confused with a much simpler concept "raising the question", it kills the original meaning so I have to explain the concept in far more words. For example, "The man is assuming a fact for granted and using a fact that follows in order to prove the original fact." is much more wordy than saying "The man is begging the question."