I understand what you are saying.
Look at it like this: my children might ask for something to eat, and I might say, have some fruit, knowing all we have is apples. In that case, I am calling the apples fruit.
Or we might have melon, which I am saving for something, and apples, in which case I would *not *use the generic term fruit, right? I’d specify apples.
In the same way, your daughter could say, Most of my friends are Christian (meaning Catholic and Protestant). If she wants to differentiate, she does need to say something like “Most of my friends are {some word other than Christian, because that includes Catholics}.” She could say, “Most of my friends are Christians, and some are not Catholic,” but the reality is that she in confusing the terms in a way which could confuse others about what she, a Catholic, is saying about the relationship being between being Christian and being Catholic.
because there are some groups out there which specifically exclude Catholics from their definition of Christian, I agree with you that this is an important point. It may be politically correct, but it seems pretty silly for us Catholics to go along with what anti-Catholics say.