Why do they want to throw people to the beasts, why not kill them?
The people have a rule in their code of conduct that says, "if there is a death, the causer-of-death must die" (Chapter 2). Throwing an unwanted member to the beasts allows him to die at the hands of nature; no individual needs to take responsibility for the death with the forfeit of his own life. The people take this rule very seriously. It is what saves Kira from being stoned to death in Chapter 2 by the mob led by Vandara.
By the end of the story, however, we discover that in reality, the unwanted are killed by the Guardians. This is what happened to Kira's father - it was Jamison who killed him (or attempted to), not the beasts. The beasts do not exist - they are part of an elaborate fable made up by the guardians to control the people in the society through fear.