When you mix red, blue, and yellow paint, you get gray. Therefore, if you consider the collective effect of adding up a bunch of even numbers, you can get an odd number. Right? Or was there some logical flaw there?

Saying "collective" and "synergistic" doesn't magically make whatever you want come true. Collective effects do happen, but they need to be documented just like everything else does. Criticizing the dogmatic thinking of mathematicians who can't see synergistic outcomes doesn't do anything to get yourself to odd numbers.