Is your claim that there is a class of people who invade homes while carrying a firearm, but will only use it if the other person also has one?

Yes, assuming "use" means pull the trigger while aiming at a person. If you get threatened by a gun then you'll be more likely to shoot. Do you find that unlikely to be true?

I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

You're evading the question. When you ask me to explain my reasoning I would normally expect you to do the same. Or just say you don't care enough to properly reply, that's also fine by me. Now you spin it back to me by implying I am some sort of idiot instead, which is not very nice.