Why did Daenerys Targaryen feel betrayed by Doreah?

Let's see the situation from Daenerys's eyes:

1. She returns to the palace to find many of her men and a faithful handmaiden (Irri) dead.


2. Not only that, but her precious dragons, her babies, missing. Her other trusted handmaiden (Doreah) is also missing.


3. She spends many days, nervous and afraid, as she looks for the missing dragons.


4. Once she finally finds out where they are hidden she has to go through an extremely dangerous and stressful ordeal (the House of the Undying) in order to get them back.


5. When she figures out that Xaro Xohan Daxos was responsible for the kidnapping in the first place, she also finds out that Doreah is safe and sound and in his company.


6. Danny deduces that Doreah had sold her out to Xaro in order to keep herself safe and win the wealthy man's favor.


7. Doreah protests that she all did it to keep Danny safe, but at this point of time she only has Doreah's word that this is true, and Danny has no reason to believe her at that moment.

In short, the whole ordeal has made Danny a less trusting person (the lesson she thanks Xaro for), and now sees Doreah as a traitor who deserves death.

Did Doreah really do what she did to save Danny's life? Perhaps. But the price (the death of Irri and the kidnapping of the dragons) was too high to justify it in Danny's eyes.

Also, in a deleted scene it is revealed that Doreah herself killed Irri with a strangling cord when Irri walked in to find the dragons in cages, so it is truly a life for a life.

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