Why does it have 1-based indexing? Historical reasons. (Cleve Moler decided so). It probably has to do with 1-based indexing being the convention for matrix notation.
Why does it not implement 0-based indexing too?
Up for some nice light reading?
In particular, look for comments from Cleve Moler (the creator of MATLAB) and Steve Lord (MathWorks Engineer). After much exchange, the basic reasoning (at least in 2001) for not implementing a supplementary 0-based indexing was not for any philosophical or compatibility reasons, although it started as a backward compatibility argument, but because it would require just too darn much effort to update MATLAB built-in functions:
I agree that it would be possible to add zero-based indexing to MATLAB,
using either new notation or an object that overloaded all of our
existing indexing notation. It could be backwards compatible in the
sense that old code that didn't know about or use the new stuff would still
work.
But here is the key point: none of our existing code would work with
the new object. You couldn't plot it; you couldn't print it; you
certainly couldn't do any matrix operations with it. Yes, over time,
everything could be rewritten to handle the extension, but that
is what we want to avoid. It would be like AM and FM radio -- two
systems living in the same box, but with separate and independent
underlying technology.
-- Cleve Moler
moler@mathworks.com
Translation: They don't want to write all new plot, print, etc. routines.
