Why is the young man in "The lady or The Tiger" put on trial in the kings arena?
The young man is put on trial for having fallen in love with the King's daughter, and having a relationship with her, which is forbidden because he is not a nobleman, but a commoner.
"For a commoner to love the king's daughter is a crime, so the king searches for the most ferocious tiger and the most attractive lady (but not the princess, of course) for the young man's trial in the arena."
Therefore, the King who punishes all offenses in his kingdom by putting the offenders in the arena, thereby entertaining himself, and those in attendance and sending a message to his subjects that if they disobey the King, they will end up facing a tiger or a ferocious animal of some kind. Although there is a chance that they will live if they choose the right door.
The young man is put in the arena to decide his own fate, choose the right door and live, or choose the door that lets the tiger loose and die in front of everyone, including the Princess that still loves him.
The young man is tried because he had the bad fortune of falling in love with the King's daughter. The king found out and decided the man must be tried. The young man is known in the story as the "Courtier" and his love affair with the princess results in his imprisonment and trial."