It's a lot safer if a random thief breaking and entering your home does't know for certain if you have a gun. For one, he won't be going specifically to steal your gun. And he won't necessarily pack any heat of his own if he doesn't expect that level of violence.
And of course there are plenty of people who would like to lynch gun owners as a matter of policy. A bit ironic, but that's the kind of hysteria the U.S. experiences every time someone goes on a rampage.