Just like your finger prints, height or face. It is uniquely yours but not your property. It's your set of attributes.

None of which are actually "uniquely yours", because everything we know to date about fingerprints or faces or DNA is that there is a low probability of collision with someone else having those same attributes, but it's not zero probability.

Somewhere, somewhen, there is likely to be another person who has a face, or fingerprints, or snippet of DNA that cannot be distinguished from yours within the accuracy of the tools we have today.

There was actually a podcast by Radiolab recently that discusses how and why this is not the case. It's counterintuitive for sure, but pretty interesting.

https://www.wnycstudios.org/story/asking-friend

What about the hair you leave behind on the subway? Or when you spit on the field during an ultimate frisbee game?

I can’t take your hair off your head, but I can take it off the ground.

What about the image of my face I left behind on the subway, or on the field during an ultimate frisbee game? Sure you can keep my image on your camera, or photo print, but you may not profit from it, because it isn't your property.

Or your breathe you push out of your lungs.

Exactly.

Which must mean that you're a thief if you've ever brushed past me on the street. Give my DNA back.