The princess might have indicated to her lover the door with the tiger behind it or the one with the bride behind it. Give one reason why she might have shown the door with the tiger behind it.

We simply don't know which door the lady sends her lover toward. That's one of the many reasons why the story retains such an enduring fascination. The princess has perfectly valid reasons for wanting her lover to choose either her or the tiger. Most obviously, it could be said that she indicates the door behind which she's standing because she wants to be with her lover. At the same time, however, she could just as easily send him toward the door with the tiger behind it because she's insanely jealous and can't stand the thought of his being with another woman. In fact, it's notable that equal space in the story is devoted to the princess's anxiety about her lover potentially cheating on her than to the terrifying thought of his being torn to pieces by the tiger.