The princess chose this door because she wants him to live and be happy knowing there is a chance that one day they might be together again. She did not want him to die or suffer at all not to mention she could not live with herself if she new that she was responsible for his death.
The princess felt that the love they shared was to strong for her to lead him to death and he knows what he would do for her so he expects the same. The princess wanted him not to mery the women but also not to die. The man’s fate was decided by her decision.