The ancient Greeks didn't think 1 was a number; as late as ~1500CE Isidore of Seville was saying "one is the seed of number but not number". After all, if there's only one thing you don't need to think of it as a set of things, so there's no counting to do.
(I think in some quarters it was even argued that two isn't a number, but I forget the details. Compare the fact that some languages treat pairs of things differently in their syntax from larger groups.)
But it turns out that mathematically it's a really good idea to count 1 as a number and allow sets of size 1, and these days everyone does it and no one is very confused by it. (Well, maybe by the "sets of size 1" thing. Exhibit A: Perl. Exhibit B: Matlab.) And because we're now all used to thinking of 1 as a number, it's hard even to understand how anyone might have found it unintuitive.
If we all started counting from zero and taught our children to do likewise, intuitions 50 years from now might be somewhat different from what they are now.
That's what it represents in indexing, the distance you have to travel to get to the element you want.
That's an offset. It's already covered in detail in TFA.
We don't deal with such offsets in programming, except in C pointer arithmetic (which infested this upon us).
People never said and still dont' say "this baby is 0 years old". They start at the first complete item of the lower level time units and progress from there...
So they may say one hour old, five days old, six months old, etc. a fifty year old typically doesn’t say they are a half centenarian either. Now decades are used to express an age range like so and so is a nonagenarian to avoid being specific.
How many more things can I fit in that box? How many comments are in that HN page?
I'd write more, but I'm running on empty and my pen is out of ink.
Well, 0-based is not what we use in everyday life, and even arriving at the invention of 0 took us several millenia, so I'd say its non-intuitiveness is pretty much established...