My understanding was that a character had a main hand and an off-hand... weapons need to be used in their main hand... the way around that is with natural weapons and of course TWF.
unless you are ambidextrous... try and use a sword in one hand with it's nuances of use and a sling... never going to happen. In this case the sling, if loaded prior to combat, would lose its load due to the movement of the offhand in combat... your off hand does not stay still as its required for balance...
I realize that this is real world physics in a game setting but it makes sense.
IMHO.