Answer:
Everyone has me and no one can lose me. What am I?
My first two letters say my name. My last letter asks a question. What I embrace I destroy.
You write on me and secrets I can keep. In places never seen. I spin like a top. Though stiff as a board I'm often described like a mop.
I tremble at each breath of air and yet can heaviest burdens bear.
The warmer I am the fresher I am.
What never gets any wetter no matter how hard it rains?