As indicated above, the 22 Short is quiet and sometimes useful because it does not "overkill / spoil meat.
However, the following also makes the 22 Short the desirable cartridge:
1) It has less penetration than the 22 LR and could prevent or reduce damage when used inside structures, i.e. when used against rodent/vermin.
2) In some target shooting disciplines, all that is needed is to punch a hole in a paper target at 50' during rapid fire, and then the almost non-existant recoil of the 22 Short is better suited thn the 22 Long or 22 LR.
3) Elephant poaching !! Yes! Not that I am encouraging this practice, but as reported by David Westerhout on p 61-63 of the January 2003 edition of the excellent manMagnum magazine (published in South Africa, and can be bought via mail), it has been done. Perhaps out of desperate need, not by choice, but the 22 Short has been used to kill several (not only one) elephant. This story (according to David) was previously related by the respected PH John Northcote in the African Hunter, Vol 8 No1).
RSA1