I have a character who has trained shortsword, sling and two-weapon style.

I can't seem to have him equipped with a sling and an off-hand sword, I can use a sling and shield, why not a sling and (one-handed) sword ?

I think it is for the logics of it...the sling is for distance fighting, and the short sword is for melee. How can you be engaged in both at the same time??. Remember that the enemy gets a +4 to hit you if you are trying to hit him with ranged weapons at melee (short) distance...

When you try to equip two Throwing Axes for example, it says you can't have a missile weapon equipped during dual-wield or something, and I think that's quite a good explanation.