Let me fix your comment:
"Even though he is clearly in the wrong (by being in your house) he does not have the obligation of simply allowing you to kill him. He may very well murder you instead."
If someone enters my house, under the principles of the castle doctrine, they may murder me if I miss, but they will never be justified in their use of force against me or my family. They need to be lawfully allowed to be in my house for any chance of them citing self-defense.