[yummyfajitas]

In short, the theorem states that in conditions that will never exist in the real world,...

If only Modigliani and Miller weren't total idiots. Then they might have repeated their calculations with these assumptions relaxed.

First they say "the value of a firm is unaffected by how it's financed", but then: "the value of the company increases in proportion to the amount of debt used", so if "debt used" counts as "financing" then the theory contradicts itself, at least as described by Wikipedia.

If you bothered to read the article, you'd recognize that Modigliani-Miller actually did the exact calculation you previously criticized them for not doing. Similarly, if you read it, you'd recognize that the claims you think are contradictory actually apply to different circumstances (taxes vs no taxes).

What next, medicine is contradictory because "if you don't eat cyanide, you probably won't drop dead, but if you do eat cyanide you will"?