To "have a way with words" has two opposite meanings, depending on the tone of voice, and the context within the conversation.
When someone is saying complimentary things to another, you might say, "Well, you certainly have a way with words, I did not like your idea originally, but you have convinced me that it is good."
In the other, when someone disagrees with you or doesn't like what you have said, such as in the sentence above about moving out, it is said in a sarcastic tone of voice, meaning that you are not being very nice.
I am not a teacher.
P.S. on edidt. Move out, just means leaving the house, room or apartment not just for a day, but to take up residence somewhere else.