This is not a stupid question at all! I understand why you would be confused about this in particular.
The root word in these is "cloth". Shoes are not referred to as clothing or a piece of clothing. They're not made of cloth, so they're just referred to as shoes.
"Clothing" and "a piece of clothing" both talk about shirts, pants, undergarments, dresses, and the sort. I don't recall hearing hats being called "a piece of clothing", so it may sound odd to call it that.
Hope this helped a bit!