Im just an anonymous person on the internet but even I can see that this can really hurt your reputation. That start of the article painting you by using a random game you had with Zuckerberg is very low. I think the previous commentor's suggestion to talk to a professional has merit.
They are effectively accusing you of destroying a multi-million company through libel... If this happened in court you'd be getting a lawyer, no? Maybe i'm being dramatic and the best way to go through this is just to ignore it and let it calm out but it's probably not a bad idea to talk to someone with a cool head and experience.
My pet philosophy is that math is real because the objects have persistent effects, like with the "if a tree falls in the forest..." riddle. Something that isn't real would be a story, because things do not have effects in it.
If a function is one-to-one, it has a (right? left? keep forgetting which one)-inverse. But if Moshe the imaginary forgot the milk, his wife may or may not shout at him, whichever way the story teller decides to take the story... So a function being one-to-one is real, but Moshe the imaginary forgetting the milk isn't.
I like this view when I'm being befuddled by a result, especially some ad absurdum argument. I tell myself: this thing is true, so if it wasn't we'd just need to look hard enough to find somewhere where two effects clash.
Well most of your examples are about failure to act based on reasoning rather than failure to reason, except the mathematics one which is unfair as research mathematics is a very hard task - either subtle errors, reasoning in new fields, or extremely long chains of reasoning.
On the other hand, a passive student will let you go through an entire proof only to raise his hand when you finish and ask something that implies he did not understand the proof from the start.
Why didn't you say so? You wasted both of our time... I even turned around a few times and asked if everyone was following!
I know it's hard to understand when you don't understand. But I don't know how to deal with this problem and the senior lecturers don't seem to know how to, either...