Baloney. "Arm yourself" doesn't make you safer. You think it does because of the "fallacy of misleading vividness"---the (rare) case where a gun is good, i.e. a Hollywood-style armed-self-defense event, is vivid and exciting and easy to daydream about; the (common) cases where a gun is bad, like when a family member becomes irrational or suicidal, or a gun is stolen in an empty-house burglary and kills someone you've never met, are boring/depressing and hard to daydream about. This fallacy makes people ignore the common but boring possibilities and mistakenly think the "vivid" possibility is common.
Even on the "vivid" side, guns are not a defense, they're an anti-defense. A burglar breaking into your house is going to ignore you if you hide or sneak away with your bare hands. They're going to get away with your cash or your painkillers or whatever and you'll be fine. If you do one thing, anything whatsoever, that falls in the category of "self defense", you've made things worse than if you'd been barehanded.
Also, "arm yourself" instantly upgrades all sorts of minor misfortunes from "embarrassing/scary story to tell later" into "one dead and one in custody". Inquisitive children (yours, visitors), drunken anger (by you, family, houseguests), mental illness flareups (you, family members, houseguests), or fear/rage/mistaken identity) from "embarrassing/scary story to tell later" into "someone is dead and I'm in jail".
You don't have to have "criminals disarm themselves". You have to get the people who sell guns---law-abiding people like you, who buy guns legally and pass NICS checks while doing so---to stop selling guns to complete strangers. Which you're free to do now (it's even legal!) but you would not be able to do if the guns you bought had a legal- or financial-responsibility-bearing title connecting the gun's serial number to your name and address.
Imagine a car-sale law that said your car-insurance would remain active until a new owner's insurance was on file. That'd make it very, very hard for anonymity-needing people to buy cars; no self-interested person would sell you one if you weren't willing to attach your own name to it. If you make it the same way with guns, and gradually (10-20y) it'll deplete the supply of (and increase the street price of) the cheapo street guns that fuel most drug/gang violence.