One thing to try is to get the idea across that "Firing Arc" is a special, defined term in the game that does NOT follow common sense. You could even go so far as to replace the words "Firing Arc" with "Blerg". Every ship has a forward-facing Blerg. You are normally only allowed to fire at targets inside your Blerg. If you equip a turret upgrade, it allows you to fire at targets outside your Blerg.
By separating the in-game concept of "Blerg" from the real-world, common sense meaning of "Firing Arc", you might be able to get him to understand the rule better. I find that a lot of people get really hung up on what they *think* a word means, so you have to replace it with a totally different word to break that barrier.
Another example of this is "Touching". "Touching" in X-Wing means "Overlapped earlier this round and haven't yet moved apart." It doesn't actually mean what "touching" means in common English. Two ships can be "touching" without being "Touching". I use "Blerg" as part of my explanation of this problem, and people tend to take that well.