So I would say communicate your feelings, and be true. However, the label really doesn't matter, if it's important to your BH.
I agree with this. Is your BS on this forum? I feel that many members here obsess over the "label" and the questions get asked, which is worse? EA? PA? ONS? LTA? And then we have to get into what defines each of those terms, and on it goes.
I don't obsess over the labels. I would use a sentence with ten or more words to describe the A more fully, if that is what was needed, rather than to try to categorize it with a one word label, that not everyone even agrees on what that label represents.
If I were in your shoes, I would tell him to call it an EA or whatever he wants to call it, and tell him that you are not going to become defensive but if he wants details, you will tell it the way you already have (assuming that is the truth, of course). Not everything can be put into a neat little category with one word that fully describes it, where most everybody agrees that one word means the same thing.