When you have an item in your inventory that you move to a storage container it unequips the equivalent item from your character and slots it in your inventory. As an example, if I have a hat in my inventory and drag that to a storage container it unequips my currently equipped hat and moves it to my inventory.
I went back and tested this. It only happens if you double click the item to move it from your inventory into storage. If you drag and drop the item from your inventory into the storage it does not unequip the equivalent item.