The big grin on the boys face is worth a million!
It's possible she felt slighted in some way if you didn't include her in the gun shooting lesson, for that you could apologize. HOWEVER, make it clear there is no way to deny learning to respect firearms, and learning firearm safety is an important lesson a young man needs to learn just like using a knife, ax, chainsaw, etc.
You should gently point out how she crushed her son's feeling of accomplishment, and that she should be proud of him and his demonstrated skill. You can explain that she should express her fears and concerns in an open conversation with her son, and realize he is growing up and needs to learn important life lessons in order to not make mistakes. Who is going to have these difficult discussions with him? Wouldn't she rather have him learn responsibility from a man she knows rather than from friends. Guns are just one little thing. There will need to be conversations about drinking, drugs, girls, etc. and at about the age he is now.(maybe not everything but...) They start "learning" a lot younger than parents want to believe. Goes for daughters too.
I started with my boys at 4 years old. At eight they knew gun safety and understood the devastating difference between T.V. and real life. That understanding is what saves lives.
