1. "He looked at me, then went off in a tangent about crime and criminals, completely dismissing my point."
That's how some people admit they're wrong. They can't say it, so they just change the subject. Very few people are comfortable saying, "Ok, you win that one, now here's my next point" but that's what he was saying indirectly.
He was admitting he couldn't answer you, which is not the same as dismissing your point.
2. One response to the "do you want my crazy neighbor to have a nuclear weapon" argument is to say that the Second Amendment protects ownership of weapons appropriate for our membership in the militia: rifles, pistols, shotguns. Nuclear weapons are more like the naval ships of the 18th century, something for the pros.
(At least that's an argument you can make. I'm not saying I find it totally compelling, since militias in the 1700s did often have cannons, but it's an argument based on the constitution and history and it gets the antis off this point, which many of them regard as rrefutable.)
The other part of this reply is that the weapons protected by the Second Amendment are those which would be useful in overthrowing a tyrant. Nuclear weapons are kind of irrelevant to that, since a state is not likely to use nuclear weapons against its own people, nor are the people likely to use nuclear weapons against one tyrant.