Re: House Rule Rebuttal: Back Shields
Ok, if he insists on being able to use it, then why not say. Ok, you can use a back shield, which when you use it, you take the armor check penalty for its use, [meaning attacks and physical skills] and you can apply the shield bonus to reducing the flanking bonus vs. one designated opponent, similar to a dodge bonus. Do note however, if I was handed that rule as a player, I'd admit, I'd at least contemplate trying to get a masterwork shield, so it its armor check penalty would drop. Just warning you.
But then you are allowing the behavior, so he shouldn't complain too much. Like you said, when you get something, it should have 'some' sort of cost. You could even give in even a little further, saying you only have to take the action check penalty when you use/become flanked. Otherwise, you ignore the shield, since it is just weight on your back like a backpack.
It is disappointing that your friend would break up a game over a ruling that [at least in my mind] makes sense. Obviously, I'm going to grant there might be a chance said individual honestly can't understand how they could be wrong. However, I honestly just don't see how wearing a shield on your back, passively, can net more of a defensive benefit, with less restriction, than wearing one actively on an arm. But I would definitely focus more on making sure the game remains fun. If that means making your game a bit comical in that sense, so be it, as long it is fun for everyone, yourself included. You could even, if you don't feel like you can just 'make the call' you could present the matter to the group to make a silent ballot vote to determine the matter.