The trouble I see in this question is that no one can ever truly know how they will react in a highly charged, life-threatening situation until they find themselves in one.
Most people in this country in these times have never faced a true mortal danger, one where they could take, or not take, an action which could change the result of the threat.
I suspect that some people who would say they could never shoot someone, when put in an actual situation, might find that they actually could. Likewise, some people who have no doubt that they could shoot to protect themselves or their family might, in an actual situation, be unable to do so.
It is a wonderful thing that the modern developed world holds so few dangers for most of its inhabitants...but it leaves us unprepared for an occasion where we might need to protect ourselves or others. The lack of experience becomes a potential problem.
I do feel that anyone who learns to use a gun for protection had better be practicing very regularly, and not just standing still doing target shooting. This is in part why I'm getting involved in IPSC (mainly for the fun!).
I really don't know how you choose who to teach and who not to just by talking to the person. Give the woman a starter lesson and see how she reacts to the gun, I'd say. Then advise her based upon that. But you'll never be able to know whether or not she would have what it takes to use the gun for defense -- and hopefully neither you nor she will ever find out. And she definitely should be made to understand that just learning the basics of gun handling and shooting and then sticking the thing in a drawer, handbag, whatever, will not be enough. Maybe the most important question to ask is whether or not she's willing to make a commitment to shoot regularly for practice to build proficiency, after you've taught her the basics.