Apart from the irksome grammatical errors in the story, I find it naive that you assume the world to operate ceteris paribus, and thus, find your argument unconvincing. In your story, you give us two viewpoints, one where one has a gun, and one where only the criminal has it. Those stories play out exactly as one would expect they play in a perfect world, but there are a bunch of variables to consider about this. I'll bring up two.
1. Gun Control Policies
In one of your posts, you cited Switzerland as one of the countries who have done gun control correctly. But there is a reason for this gun control. Switzerland, as was stated here somewhere, has a militia. Swiss males are expected to undertake it at age 20, and they are taught the basics of gun safety, and even required to keep their army-issued weapon if enlisted, or a 9mm pistol if you're one of the law-governing units (police, etc.) at home. Also noted is that every single Swiss male is considered to be a militia reserve until the age 30. This gives Switzerland a different gun policy than most countries.
2. Law Enforcement
By this, I mean just how strictly your country enforces the law. Some countries find killing an individual a no-no, and you may be tried on court until you can prove it is entirely justified self-defense. Obviously, some people would find doing this much of a hassle if they're not directly involved in the situation, so not everyone with a gun could suddenly pop out and fire at a criminal. As far as I'm concerned, in the Philippines, killing is murder unless you can produce evidence to the contrary. A lot of us are below average the normal living standards, and thus we don't wish to see the court too often as it drains money way too fast.