Polydectes is able to trick perseus into battling medusa because of perseus’s :

noble birth
supernatural gifts
divine assistance
excessive pride
skill at fighting

The answer is: excessive pride.

Perseus is tricked by King Polydectes to fight the Medusa in an attempt to get rid of him in order to marry his beautiful mother, Danae. Pretending to have the intention of marrying another woman, Hippodamia, the King requests gifts in the form of horses to be brought to him. Perseus is unable to provide the gift but asks Polydectes to name whatever other gift he wishes so that he can reestablish his honor. The King asks for the head of the Medusa. Since Perseus, having previously boasted of his gifts as a fighter, even claiming to be able to slay the Gorgons (Medusa being the only Mortal Gorgon), accepts the challenge out of an excessive pride. He does slay the Medusa and, when he returns, turn Polydectes into stone by showing him his victory trophy, the head of the Medusa.

the answer is the speaker views both as possessions that reflect his importance.