I see what you are getting at, and it does make sense.
On the flip side, would you rather rob a home that is absolutely 100% assured to be gun-free, or would you try to rob the home of a well-armed citizen? The citizen is on the defense and you're trying to sneak around. When the burglar and home owner are equally armed, there is an inherent advantage of being on the defensive. If you take away the home owner's gun so now only the criminal has a gun, the balance of power shifts in favor of the criminal.
As to whoever asked why the US has lots of crime despite everybody owning guns, that's only half-true. While many Americans own guns, most states do not have concealed carry laws, which means a good 99% of citizens walking around are not carrying guns at that time. If you point at some random person on the subway, you can bet your life on the fact that he does not have a gun on him, assuming you are in a state that does not allow concealed weapons. If you're in a place like Texas, it might be the other way around (Texas allows concealed weapons).