Nononono...he wants to ski with her in the future. It's getting her to the point that she can hang without breaking up first.
Your own qualifications as an instructor are not at issue here. You are the boyfriend and at some level your constructive criticism is just plain criticism and is personal. She will not be objectively listening as she would with an instructor. Instead she might get hurt by constant cues coming from you (and they will be constant because she is just learning).
I want to learn to tele and my boy rips on tele. But by no means would I want him to teach me from the beginning though I have alpined for 27 years and am athletic. The reason being that I know how frustrated I become when I am learning new things and I would rather have a total outsider guiding me through the process who has no personal investment in me. It's just easier that way. But once I get it down, I want to continue skiing with my boy who can give me good tips and sets a good example (on skis...).
Simplify your life and let someone start from the beginning and then take her from there. I think she would appreciate that.