Killing the bull has been outlawed in some countries for its cruelty, but ironically, the most hurtful parts of the fight(The placing of the bandarillas and the stab with the lance, are still part of the fight. In most countries, the bull is killed by the matador.
The reason why the bull is killed in the arena is because the entire match plays out much like a classical tragedy. There are two adversaries. One of them, the man, has the skills and knows what's going on, while the bull has the strength, and although it doesn't know what's going on, is a very fast learner.
That's part of the reason why a bullfight may never take more than 25 minutes. If it does, the bull is taken out and killed like ordinary cattle.
Anyway, the bull can kill the man, and the man can kill the bull. The man is required to go through the three stages of the fight before he can kill the bull, while the bull can kill him at anytime. If the bull wasn't killed by the matador in the end, it would be like if Romeo and Juliet ended BEFORE the suicide; there would be no resolution to the conflict.
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That is the goal of the matador, to kill the bull and escape unharmed. It also serves a practical purpose. A bull can only be fought once because it would be too knowledgeable and too dangerous to use again. It prevents unscrupulous bullring managers from 'recycling' animals. The only bulls that might be recycled are bulls that are pardoned for a superior performance in the ring but they are sent back to the ranch to be used as seed bulls and are never fought again.
Killing the bull is the ultimate purpose of the bullfight. There is another purpose. Legally, a bull may not be recycled. It cannot be fought again. Since a bull learns quickly that the cape is not the enemy but the man, it would be quite dangerous to use the bull in another bullfight.