Why is killing a brahmin considered sin while killing other caste people is not?
Your confusion arises because you think that Hindu scripture supports the Hindu caste system as seen today. That is not the case. The term Brahmana in Hindu scripture has a different connotation from the Brahmana of Hindu caste system. Hindu scripture is talking of Varna which is dependent on conduct.
Bhrigu said, 'He is called a Brahmana in whom are truth, gifts, abstention from injury to others, compassion, shame, benevolence, and penance. He who is engaged in the profession of battle, who studies the Vedas, who makes gifts and takes wealth (from those he protects) is called a Kshatriya. He who earns fame from keep of cattle, who is employed in agriculture and the means of acquiring wealth, who is pure in behavior and attends to the study of Vedas, is called a Vaisya. He who takes pleasure in eating every kind of food, who is engaged in doing every kind of work, who is impure in behavior, who does not study the Vedas and whose conduct is unclean, is said to be a Sudra. If these characteristics be observable in a Sudra, and if they be not found in a Brahmana, then such a Sudra is no Sudra, and such a Brahmana is no Brahmana.'
Mahabharata, Santi parva, Section CLXXXIX
One can not be a Brahmana by simply being born in a Brahmana caste.
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