What is the reason for rmdir(1) and rm(1) to co-exist?

I use BSD and Linux every day, I have never had a circumstance which I must use rmdir(1) rather than rm(1). What's the purpose of rmdir's existence?

The main reason is probably historical. Back in the old, old days, there were no rmdir(2) and mkdir(2) system calls (we're discussing 7th Edition UNIX™ here), and rmdir(1) was (of necessity) a SUID root program that used the unlink(2) system call to remove directories.

The 7th Edition UNIX manuals are available online at http://cm.bell-labs.com/7thEdMan (last checked 2017-04-23); They are also available at http://plan9.bell-labs.com/7thEdMan (last checked 2017-04-23). There also seems to be at least one alternative source online — http://wolfram.schneider.org/bsd/7thEdManVol2/ — for the articles in Volume 2, with a link to the FreeBSD site for the commands and system calls in Volume 1.

The rm command (a regular non-SUID program) invoked the rmdir(1) command to remove empty directories. It could not do so itself; that required root privileges. So, the rmdir(1) command (see here for its source code in Unix V7) existed to remove empty directories, and the rm command did not remove empty directories itself.

To use rm to remove directories, you have to give the -r option.

There's also a symmetry argument. You need a command mkdir(1) to create directories; it seems reasonable to have a command rmdir(1) to undo what mkdir(1) did. Plus they are (these days) simple exercisors of the the rmdir(2) and mkdir(2) system calls — yes, back in 7th Edition UNIX, mkdir(1) was also a SUID root program, using the mknod(2) call to create a directory node and the link(2) call to create the . and .. entries in the directory.

"rm" does not work on directories. You have to either use rmdir or specify the -r switch for a recursive deletion. The reason is historical: unlink and rmdir are separate system calls and have been from the early days of Unix.