In response to the second part of your post:
It’s really hard to truly "convince" someone to get scuba certified especially if they are afaraid of it. In my experience, there are a lot of women (and some men too) who sign up for a scuba class because their SO is a diver, not necessarily because they want to. Those students tend to be a little more skittish.
I think your best course of action will be to promote the positive sides of diving - why you love it and what you think the advantages are over snorkeling. Also, consider signing her up for a one-on-one pool session with the instructor so she can try out the equipment and see how she feels without the pressure of being around other students and comitting to a class.
All that being said, I have a friend who learned to dive at her husband’s request and was terrified. Now she’s an intructor.