Would you keep a friend that asks when you say..."well, a ?

friend of mine blah, blah blah"...and she asks, 'WHAT FRIEND?"...and you and are taken back by that. and just say politely.."oh just a friend."..or when you are talking and she mentions, "what happened to so and so...How did it happen?,,,,and you say.."oh geez, I would never ask that. and she says.."why?"..she is a WHY PERSON. You say..."because it is tooo intrusive."...She does bother me to where I get sooo upset but do NOT show it. I feel i need to let her go, shoudl I?