Here's why:

* Lives in a forest: Trees are a defining feature of forests.

* Does not move: Trees are rooted in the ground and do not move independently.

* Has bones: While not literal bones, trees have a strong internal structure of wood that provides support.

* Greenish-greyish: The bark of many trees is a shade of green, grey, or a combination of both.

Let me know if you'd like to play another riddle!