How does Perseus come to claim Andromeda as his wife? Why does Cepheus object to this?

The Ethiopian king has chained his daughter to a rock by the sea.

Perseus quickly flies down to help Andromeda. At first, he tries to engage her in chit-chat, without much success. Then, all of a sudden, a huge monster arises out of the deep. It is coming to eat Andromeda!

Now Perseus sees his chance. He calls out to Andromeda's parents, the King and Queen, and says that, if he kills the monster, they have to accept him as their son-in-law. They agree to his terms.

As you might expect, Perseus battles the monster and kills it.

During the celebrations that follow, Perseus puts the head of Medusa on the sand. So that it isn't damaged, he makes a bed of plants underneath it; then he puts the head face-down on top of it. As it turns out, the plants soak up the power of Medusa's eyes, and turn to stone. When Perseus throws them into the sea, they become the first coral.

Then Perseus makes sacrifices in honor of the major gods, and claims Andromeda as his wife. At the wedding feast, someone asks him to tell how he killed Medusa.