Beats1 on Mac doesn’t start unless I logout
I know this situation. Even if you use the correct Apple ID to authorize music playback, you may still see a repeat request for authorization. This can happen if you're logged in to your Mac using a simple user account, which doesn't have the correct privileges to allow iTunes to update its internal files with the authorization information.
    The solution is to log out and then log back in using an administrator account. Once you're logged in with an administrator account, launch iTunes, select "Authorize This Computer" from the Store menu, and provide the appropriate Apple ID and password.
    Log out, then log back in with your basic user account. iTunes should now be able to play the song.