Why the tiger came out of the door?
Similarly one may ask, did the lady or the tiger come out of the door?
So her lover chose the door that she indicated, Frank Stockton tells us that much. Personally, I believe the tiger came out. The princess would not stand for him to be married to another woman, and would most likely rather have him killed than lose him.
Subsequently, question is, what is the conclusion of the lady or the tiger? The Princess hates the woman behind the door. In the story, it says the Princess chose the "right door," which could be interpreted as the "correct" door, or the morally correct choice. The Princess loves the man, and cannot bare the thought of him being eaten alive by the tiger.
Keeping this in view, why would the princess choose the lady?
Reasons the princess chose the door with the lady behind it. She loved her suitor enough that she wanted them to be happy. She could still see the suitor and be friends. She wouldn't have to deal with the guilt of his death.
What is the answer to the lady or the tiger?
Here is the answer to the lady or the tiger puzzle: the prince should pick the other door. If he sticks with the first door he picked, he has a 1/3 chance of finding the princess behind it. If he picks the other door, his chances double to 2/3. Don't feel bad if you didn't quite get the answer.