As a friend, Owen had to fire Teddy. It sounds weird, but it makes sense. Teddy was going to pass up a lucrative position with the Army to stand by Owen in his time of need. Owen couldn't let her pass up an opportunity like this and gave her no choice but to accept the job offer after he fired her. In tearful parting words Teddy told Owen to fight for his wife because Cristina was considering taking a job with the Mayo Clinic. If Cristina took this job, there was a chance Owen would never get her back. Unbeknownst to Owen at the time, Cristina and the rest of the survivors of the plane crash were fighting to stay alive.