The child, Perseus, is the son of Zeus. That is why he is to be saved and why Argos is doomed.
13 seconds sound clip from the Clash of the Titans (1981) movie soundboard.
You can hear this line at 00:07:44 in the Blu-ray version of the movie.
Quote context
[...]
- Zeus, your husband, loved the girl.
- Then why should I show any compassion? Let her drown! And her child with her!
- The child, Perseus, is the son of Zeus. That is why he is to be saved and why Argos is doomed.
- Danae and her child have been brought safely to the island of Seriphos.
- Seriphos... There let Danae and her child live, safe and happy.
- Perseus, grown to a young man. He's had a happy childhood.
- And what of my son, Calibos?
[...]