Why do loading screens spin?
The spinning indicates as you mentioned, a feedback to the user that the it is busy and working on loading/getting whatever that was requested. To your own question, let me ask you this - How will you know that the computer is busy working on your request if it wasn't animated?
What is the spinning loading thing called?
A throbber, also known as a loading icon, is an animated graphical control element used to show that a computer program is performing an action in the background (such as downloading content, conducting intensive calculations or communicating with an external device).