Dropping an item without destroying it is essentially the same as trading it, because then you could just drop it and have a friend pick it up.
And trading quest items is not possible because it ruins the whole point of them being quest items. Quest items are unique and are only acquirable if you complete a certain quest. If you enable trading you might as well have a vendor that sells them and you can just complete a quest with zero effort, not to mention that the other player won't be able to.
If it's not an item that's required to complete the quest but a reward, it's still logical to make it untraceable because they want you to complete a quest to get it, instead of just buy it from another player. I hope that clarified things for you.
By the way - I also play the game with my girlfriend as a team. The way we do it is we help each-other by creating a group and hunting together.