If by fiat I can snap my fingers and all guns would disappear, the number of those killed by guns would go to zero, indisputably. The rate of those killed by other means at all relative to guns would go DOWN.
Why? Because the guns no longer exist, those in anger situations would either find other means to exact vengeance if they really mean it OR they simply will cool down and not enact any vengeance at all. Thus potential killings that would happen in the heat of anger simply would not happen at all. Also, all the accidental gun deaths...kids finding their parents guns would not be possible, no accidental people shooting themselves. No intentional people shooting themselves. There would NOT be a 1:1 conversion from deaths by gun over to "death by other means", there would *always be* fewer total deaths as a result NOT more. ALWAYS.
If however I did the reverse, I snapped my fingers and every single person had a gun. The rate of murders would go UP.
Why? Because the random events that happen to all gun owners would increase relative to the available population. You'd have all of a sudden a bunch more people who shot themselves in the groin, or kids that found their parents guns and shot their friends by accident or other accidents. You'd have more self murder via suicides. You'd also have more murders from people who get angry and use their personal gun to enact vengeance...one they would otherwise not have if I hadn't gifted to them with a snap of my fingers. Sure, it means they'd have to get the drop on who ever they are angry at (since they'd have a gun) but that's the problem...guns make it easy to go from anger to some one being dead. The opportunity cost for using them once they are had in such situations is lower simply because they are present...so there will always be an increase here. ALWAYS.
Try as I might I can't find a flaw in the absolute rates argument as I'll call it above, it clearly demonstrates that when comparing the two scenarios that the "all guns" scenario is ALWAYS worse in terms of deaths caused (by any means) so that being the case how can any one rationalize enacting it? I've found often the arguments are couched in terms of a desire to protect themselves against imagined evils (as was the case unfortunately for Adam Lanza's mother who trained him in shooting guns). This of course is a personal fear that stems from a paranoia over being the potential victim of violence but it neglects the fact that the "right" they claim to carry a gun to protect themselves comes necessarily at the possibility that a child kills himself with his fathers gun by accident or that a deranged teen gets a gun and kills dozens of babies while they are at school. Those are costs that are not worth any individuals "right" in my view...and to those that still uphold that right I say they also have the blood of the innocent on their hands for supporting it.