Why are UNIX/POSIX system call namings so illegible?

It's due to the technical constraints of the time. The POSIX standard was created in the 1980s and referred to UNIX, which was born in the 1970. Several C compilers at that time were limited to identifiers that were 6 or 8 characters long, so that settled the standard for the length of variable and function names.

Related questions:

• Why is 'umount' not spelled 'unmount'?
• What did Ken Thompson mean when he said, "I'd spell creat with an 'e'."?
• What, if any, naming convention was used for the standard Unix commands?
• https://stackoverflow.com/questions/682719/what-does-the-9th-commandment-mean

dr01 is right, but there's also another reason - usability. Back in the day, you didn't have something as comfortable as a keyboard to type on. If you were lucky, you had something akin to an old-school typewriter. If you were unlucky, you had to deal with systems that required actual physical work to operate (as in, it took a lot of force to press the "key"), or you manually punched holes in a card.

This meant that even within the 6-8 character limit, you tried to keep your commands as short as possible. That's why you have ls instead of list, and creat instead of create. Code from that era is full of variables like a, x and i - and of course, x2 and friends. Typing was a lot of work - today, you're less exerted from typing listIndex than you used to be from "typing" i - and it isn't even all that slower anymore (especially with additional technologies like auto-completion).

The real question is - why do so many Unix idioms persist even though they're no longer desirable?

In addition to the other answers, I would like to point out that Unix was developed as a reaction to Multics, CTSS, and other contemporary operating systems, which were significantly more verbose about their naming conventions. You can get a feel for these OSes at http://www.multicians.org/devdoc.html. For example, http://www.multicians.org/mspm-bx-1-00.html gives change_name as the command for renaming a file; compare Unix mv.

Also, the principal reason why the very short system call names persist is backward compatibility. You will notice that newer APIs tend to be more explicit; e.g. gettimeofday and clock_gettime instead of just time.

(Even today, using whateverIndex instead of i for a loop index is an automatic code-review failure in my book ;-)