So, this whole “Collatz Conjecture” thing

This just reads like "I can't find a counterexample and can't think of a way to find a counterexample so there must be no way to construct a counterexample so there are no counterexamples" and there are two points where you can go wrong with that kind of argument

"I feel like I just did, but if that didn't satisfy you, dear mathematician, I find it ironic that when I tell people they can't prove my pants weren't stolen by a pink, time traveling unicorn, I'm told that I'm "scaring families" and that I "need to leave this Arby's before the police get involved", whilst YOU..."

This is really the crux of the proof: an assertion that they don't need to take on the burden proving what they set out to prove. It's more of a challenge to us to accept what they've written as a proof or otherwise suffer social stigma for being too picky in demanding rigid arguments.

This article argues that a sequence shouldn't blow up to infinity. Does it make a case for why a sequence shouldn't get caught in a permanent loop before it can drop to 1?

This doesn't seem like a proof. It's a statistical argument? I'd tend to agree with the 'conclusion' (that all numbers collapse to 1 under the rules of the game) but I don't think its going to win any cash prizes.

i can’t tell if this is satire, but just for explicitness: this is nowhere near any level of acceptable mathematical rigor