Answer:
In "The Lady or the Tiger," the door that bothers the princess the most is the one which has the lady behind. The reason is that the princess hates the lady because she is very beautiful. Besides, when the lady spoke to the princess' lover, they smiled at each other, so the princess is paranoid about her lover falling in love with the lady more than being killed by a tiger.
What is the question you were given to answer for your essay? Just asking because I need specificity ;)
