Right-clicking on an Amor piece will make the previous one disappear.

What I expected to happen was...:
 When I tried to change my Iron Chestplate to a Diamond one, I was expecting the Iron Chestplate to go into my inventory. 

What actually happened was...:

It disappeared completely.

Steps to Reproduce:
1. Go into survival mode and get two pieces of Amor (used for the same body part).
2. Equip the first one.
3. Then (without being in your inventory) equip the second and you will see that the first one has disappeared.