Well, teach her anyway. You might be surprised. Most people are “fight or flight” and if flight is not possible, they can be the fiercest fighters. People don’t realize how dangerous a doe can be. Lots of hunters have been killed by an angry deer. Ask her if she’d shoot someone to save your life, and you’ll have your real answer.
There are such things as urban areas where the local politcos do not believe that the peasantry should own handguns. A pump shotgun is an excellent alternative. While I have not had an opportunity to check out these low-recoil defense loads, I do like Winchester Light Trap Loads. Across the room, they are nasty but overpenetration is not a problem. One might want to consider pistol-caliber Lever carbines as are used in Cowboy Action Shooting but they can be pricey.
I have done some instructing and, by and large, I have found women to be easier to teach. Many of the male instructors I know agree with me.
And, lastly, never, ever, ever underestimate what the female of the species is capable of if you piss her off badly enough.
My Democrat, gun hating mother-in-law asked me if I could shoot someone and kill them, I told her I wouldn't own a gun if I didn't think I could and would do so with no doubt in my mind. Her husband asked her, you wouldn't shoot someone to save my life? She said, No, it would be bad karma. Go figure.