I go to the store and buy a pencil. Now I have apparently 1 pencil worth 1 fiat and someone else now has 1 fiat? What a preposterous notion!

The pencil was made with 'work'. You exchange existing work with 1 fiat.

If you do not consume this work, you can exchange it back.

The cryptocurency was also made with work. Hardware, electricity, and time were invested into the 1 unit of crypto. It's literally called Proof-Of-Work.