Both arguments rest on the premise that “we” (meaning: central authorities in the government) get to decide for the rest of us what is appropriate to have. (When in doubt, always – always – reject their premises and substitute your own. Control of underlaying assumptions/premises/assumptions is how the other side steers things to their conclusions. Not that the “man on the street” thinks of it this way – they just adopt, and reflect, the narrative frame that comes from the top; they also often think of themselves as “questioning authority” when they accept the establishment’s narrative frame).
Put it to them this way – it’s one thing if the ‘we’ in question is a group of friends discussing things but leaving each other free to make their own decisions. It’s another if the “we” in question is a government deciding for the rest of us the definition of our rights.
You can also toss something like this at them – and no, it’s not a nonsequiter. This is a relevant counter-argument for the type of person attracted to this site, at least.
As for the “loose gun laws lead to gun violence” argument, Peter Hitchens (Christopher’s conservative/peace-oriented brother) frequently makes the point – in the context of British debates – that Britain in the period before WWII had virtually no gun control laws: British law on guns, then, make today’s laws in, say, Texas look restrictive. Yet there was hardly any gun violence.
(His books, including A Brief History of Crime are worth looking into; while he’s no libertarian at all, he often makes the point that the increase of law and prevalence of government officials have gone hand in hand with a crime explosion, and these laws are often turned not against combating true crime – violence, fraud, thuggery – but against otherwise peaceful people, especially people who think they have some right of self-defense, because it’s easier for the officials to go after them than tackle traditional crime).