I was veritably crying, laughing so hard at some of these "examples" of how two and two sometimes don't equal four.
For example, if you have two factories with two machines plus half a machine each, and join the factories, now you have two and two machines equaling five! Or how about the people changing bases, and thus somehow saying that math is subjective? "Well in base 2..."
No sweetie, the rules of math are still absolute: comparing one base to another and trying to say "a-hah!" is just a shell game.
That thinking reminds me of the French guy Molyneux debated once, where the former said to the latter "your logical argument isn't universal if you jump through a wormhole into a dimension which doesn't use Euclidian geometry." Molyneux had to continually reign the guy in: "Let's stay in this universe because if you make up infinite fantasy ones we'll be sitting here for the next seventy years."
All of this is why I home school: these are the kinds of people who would be teaching my kids!
It's the tactics of a small child-- get pedantic when you don't like the answer. My son when he doesn't want to do his school work: "You said sit down, you didn't say where."