So I would guess you don't understand why people make the mistake that "if not Q, then also not P". Do you have another hypothesis for the origin of this mistake? (Perhaps there is more than one cause, ha ha.)

Later edit: The first sentence had an obvious error. In the quotes, I meant to write, "if Q, then P" -- or, more symmetrically, "if not P, then also not Q" as the mistake that is often made from "if p then q".

I'm actually in large agreement with you about what "p implies q" means in ordinary English, but can wobble back and forth with some effort. Let me try a little harder to convince you of the interpretation I've been arguing.

Let's suppose you are told, "if P then Q". In everyday life, you can usually take this to mean that if Q then P because P would have caused Q. If Q could instead have been caused by R and R was likely, then why didn't the person say so? Why didn't the person say "if R or P then Q"?