The argument for 1-based indexing with inclusive upper bounds is that binary heaps are easier to write this way. Edit: And that people who are not primarily programmers may find 0-based indexing weird.
Alas, if just our forefathers had called it "offset" instead of "index".
Nope. The argument for 1-based indexing with inclusive upper bounds is that, to express ranges, exclusive indexes require you to have a bogus just-one-beyond-the-largest-valid-index element and a way to get the successor for every index. This is a giant PITA for anything but integers (MAX_INT, and x+1), which is why every single programming language I can think of also has end-inclusive ranges in some contexts. If you don't believe me try writing regexps with end-exclusive ranges.
On the other hand, there is no natural way to express empty ranges with 1-based indexing.
Going by popularity, 1-based indexing is the established convention.
0-based languages are in the minority as far as installed base and usage goes. Being 1-based is a decision dependent on target audience and application.
Fortran, one of the earliest languages, is 1-based, so there’s plenty of historical precedent.
Matlab, one of the most commercially successful languages in history is 1-based, so it’s not exactly a barrier to adoption.
