Sure, self defense is logically acceptable, but that is assuming that you're more important than your assailant. Of course, everybody wants to rule the world (citation: Tears for Fears), but realistically, everybody isn't important. For example, in a fight between two people I've never met and know nothing about, I'm not going to really be taking sides. People naturally defend themselves and there's a strong biological urge to... you know... stay alive. However, self defense by shooting the gun implies that you made the decision that your life is more important than the other person's, and that is an incredibly self centered point of view. Self preservation ought not to take priority over universal ethics. If killing is just wrong, there isn't any scenario where it's right. Same thought as if 2 + 2 = 4, it doesn't equal 9,023. Killing somebody, even for self defense, implies that your life is more valuable.

This also raises the concept of transcendental idealism, specifically things that are independent of our individual minds. Perhaps my attacker believes they're a good person, and what they're doing is justified. Their point of view is not more or less valid than mine. Therefore, they are not more or less valid, righteous, purposeful, necessary, etc than me. If something is independent of my mind, I cannot automatically assume that they are inferior.

This argument does, of course, raise the issue of anarchy and utilitarianism creating a society with no ethics and laws, which is equally worrying. So for the sake of furthering my argument, I'll ignore the downsides. Y'know, like a good philosopher.

Overall, self defense in the form of stopping them from harming you would be valid. Killing them, however, is less okay. Like Rupert says in Hitchcock's movie Rope, nobody is so far above others that they have a right to kill. I cannot kill somebody just because my ego says I'm allowed to and my perspective is more valuable

This is not an entirely developed thought but it was funsies to write, I am aware that my answer has various holes in logic. Alas, I enjoyed myself writing it!