Cap'n Pigeon,
Can you demonstrate that...
Yes: "why" means "for what purpose or reason". To have a purpose or reason, you need to demonstrate first something capable of having a purpose or reason.
"How" on the other hand just means "by what process", which is only as far as you can go without begging the question.
Suggest you try a dictionary the next time you're confused.
...or is it more New Atheist arsepull?"
"arsepull" is just a typically scatological diversionary tactic you try when you cannot deal with an argument that undoes you.
Before I offer apology
Yeah right. have you forgotten the Vlad family motto: "Never explain, never apologise"?
Are you a) admitting that some things are uninvestigable because they are beyond the scope of science?
B) Because they are supernatural or beyond nature.
You can't "admit" something you've been given no good reason to think to be true. I have no idea how you'd define, investigate or verify claims of a "supernatural", and nor have you. That's your problem.
C) They are natural but are uninvestigable because science does not yet have the means...
That's certainly true, That's why we have people called "scientists" busy researching to find out more.
... but will have.
That's unknowable. It's also the lie on which you rest your false accusation of scientism.