grey's anatomy.S6E13 I Like You So Much When You're Naked
after listening to her opera singer patient with lung cancer explain how badly he needs his work, she tells Teddy that between fulfilling her gift and a guy, she chooses her gift.
When he finds out that Izzie's scans are clear, he tells her how happy he is for her, but that even though he's no saint he deserves to be with someone who will stay.
So she decides to leave again, even after Meredith giving Derek the OK to go to the hospital board means she has a job again.
