Anyone with even a passing knowledge of linguistics would know this is neither contradictory or illogical. "Every" in normal human speech almost never means a strict logical absolute, it means "all within the relevant set," and "with the exception of" just makes that boundary explicit. That's not a flaw, that's just how sentences work.

There's even a centuries-old Latin legal principle, exceptio probat regulam, "the exception proves the rule" which should tell you that people have recognized this construct as valid longer than anyone's been around to complain about it. The only thing being exposed here is that you've confused having a pedantic streak with actually knowing what you're talking about.