The flat mixing paddle is stuck in the mixer and can't be removed from the socket. It turns but when I pull it would not come out.

Here's what really happens. The hook has a shaft screwed into it with bayonet fittings that lock into the mixer. The shaft has a locknut where it screws into the hook. If the locknut becomes loose then the shaft can screw in too far making removing from the mixer almost impossible. Try to get a slim wrench onto the locknut and loosen it off enough to allow the hook to be unscrewed. After the hook comes off, move the locknut down the shaft until the whole assembly can be removed from the mixer. Re-attach the shaft to the hook making sure that the exposed portion of the shaft is long enough to allow for easy removal from the mixer. Tighten the locknut and you will never have the problem again.

Try push it in and then pulling. Try removing it with the machine up side down or try different angles of holding the mixer a slightly shake it to release the mechanical locking mechanism. This is either broken or it is stuck. If you get them out try cleaning inside with alcohol.