Because "new book" could imply that this copy of the book is new, or that the book was only recently published, or it could mean that this copy, regardless of how recently it was printed, was just acquired by the person and they didn't know about it's existence beforehand. "New to me" clarifies that it was the last of these options that was the intended meaning.

I appreciate that, it is my new thing!

But too many online reply "Pfffft! That's not new, it's been around for a year!", so some of us try to head them off.

Tactics Ogre