What does these quotes mean with regard to The Lady or the Tiger?
"And so I leave it with all of you: which came out of the opened door-the lady or the tiger?"
"If you decide which it was-the lady or the tiger-you find out what kind of person you are yourself."
The first of these quotes is the last line of the story; the second must be one written by a teacher or a critic.
"The Lady, or the Tiger" is an unusual story because the author, Frank R. Stockton, leaves the ending to the reader. The second quotation indicates that since the reader has to end the story that is written as an "allegory of human emotions" as one critic writes, the ending that the reader chooses indicates whether the reader is one who enjoys passion and cruelty and revenge, or whether the reader wants the sympathetic ending.
As the narrator of the story explains, the answer
...involves a study of the human heart which leads us through devious mazes of passion, out of which it is difficult to find our way.
Certainly it is difficult to determine which door the semi-barbaric princess will point to because while she loves the courtier, she is also barbaric enough to wish harm to the damsel of the court selected to become the bride behind one of the doors. For, as the narrator observes, "the princess hated her."
Thus, the second quotation above suggests that if the reader is one who has no faith in the altruism of people, this reader will feel that the princess will continue to entertain her jealousy and hatred for the damsel, so she will point to the door of the tiger, convinced that if she cannot have the young man, the damsel, whom she despises, certainly will not, either.
On the other hand, if the reader is one who believes in the goodness of people as a strong force, then this reader will have the princess point to the door behind which the damsel waits. These readers will feel that the princess loves the young man enough to want him to be happy and alive, even if she cannot be the one who makes him happy.