Izzie is an emotional person who just lost her best friend and nearly died herself. Then she was scared of getting fired.
CHIEF, in this emotional state, practicaly TOLD HER that Alex didn't have confidence in her skill. CHIEF MISLED her.
Alex is a good guy. Izzie cares about him very much. But right now, she feels betrayed that the person closest to her got her fired. Everyone thinks that she is weak because of cancer. Alex is a doting husband especially because he nearly lost her.
She needs to know the truth about Alex. But until she does, she is going to belive that firing was because of him.. Cant blame her. But I do hope that the truth comes out and Izzie will apologize and Alex will accept
And Reed will go to hell. With Chief.