Sir, you are terribly wrong.
a) “But the answer to our problems isn't more guns.” — So what do you think is? How should average, law-abiding citizen defend himself and people close to him against armed bad guy? What if the average, law-abiding citizen is a small woman? Police can't do it, laws can't do it, Batman could do it if he existed, but he doesn't.
b) “The research shows that fewer guns means fewer gun-related deaths.” — Nope. This is plain wrong and there is no research or statistics that could support this claim. Usually fewer guns means more crime, violence and violent deaths. Not vice versa.