But in all seriousness, the counter for carrier spam is easy. I just did this in a game, so it works.
Build a few fighter squadrons yourself. It doesn't need to be a massive swarm. 1/4 to 1/3 of the enemy's total number will do. Almost the entire rest of your fleet should be frigates, but throw in a few heavy hitters. (Like your capital ship and a few missile craft or illuminators.) Don't bother with many flak ships, if you do at all. You should have at least as many frigates as he has carriers. A few more than is better though.
Tell all your frigates to destroy his carriers. They shred them pretty easily, and they're faster than the carriers so they can't be kited.
Meanwhile if his fighters engage your fighters, it'll buy your frigates time to destroy the carriers. If the fighters engage your frigates, then their fighters will be shreded by your smaller force of fighters.
Meanwhile your few heavy hitters can engage his few heavy hitters. (He's spamming carriers, so there shouldn't be many.