Nothing is wrong with saying or writing it, but a lot of people are mistaken about its true meaning. It does NOT mean "to prompt or invite the question", although this is a common misuse. In fact, it relates to a type of flawed argument, whereby you avoid addressing the question, by ASSUMING something already to be true.
Begging the question is what's called a logical fallacy where something is assumed without actual proof, like saying "she's ugly because she is unattractive". There is nothing wrong with using the phrase, it's just the use of the fallacy that's not accepted, because it is shoddy logic, lazy thinking.
People use this phrase incorrectly to mean "raises the question." An example: "He says he hates that show. That begs the question of he always watches it."
In fact, "begging the question" is a kind of logical fallacy using circular logic. If you say, "I hate crayons because they are not likable," you are begging the question.