As the title suggests, this is a case referring to a chest. It sort of bugs. I feel confident in saying that it isn't meant to be this way. Aka broken.

Summary:

A chest is smaller than other blocks, it isn't a fully sized block. So when you add a trapdoor on it, go forward to the chest, close the trapdoor and your character will drop onto the floor and do the swimming-pose. This is probably caused due to the chest's size. As it doesn't fill a entire block in width. The trapdoor is forcing you down since it is wider than the chest. 

Tossing in a screenshot below,

Thanks in advance,

Have a good one.