If you have the items you are trying to drop equipped on your item slots the game won't allow you to drop them. So unequip the item and then drop it, as for sliding just hold B when on a ladder and your character will slide down. --- The Bird of the Hermes is my name, eating my wings to make me tame.
thesticker posted... Hold B to slide down the ladder
In your inventory menu, press X on the item you wanna drop and go to "Drop Item"
A, not X.
And you can't be holding up or down when you hold B to slide. --- You can't make an omelette without crushing dozens of eggs beneath your steel boot and then publicly disemboweling the chickens that laid them as a warning.
As others said hold b on a ladder to slide. However as with quite a lot of the controls it's fairly tempermental. Basically you can't be moving at all and also seems that if you press B before your character has finished the animation of getting on the ladder then it won't work.