Why is killing a clansman a crime against the earth goddess?
I can't speak for the Earth goddess Ani, but any killing--intentional or not--is going to upset the tribal elders, the priestess Chielo, the family of the victim, and the killer himself. In short, the goddess validates the decisions of the tribe.
So says Enotes:
Okonkwo seeks to overpower his mediocre chi by working hard. He is profoundly afraid of failure. As a result, he is unable to balance the feminine energy of love with the masculine energy of material success. Okonkwo often suppresses his feminine side as he pursues his goals and angers the Earth goddess Ani. His rage, inflexibility, and fear of appearing weak like his lazy father, the musician Unoka, consistently overshadow his respect for his community.
I will say that Okonkwo had angered all the aforementioned, and the killing of a clansman forces their hand to exile him--all in the name of Ani. Okonkwo had angered the tribe by beating his wife during Peace Week and killing Ikemefuna when he was told expressly not to. The accidental shooting causes an imbalance in the tribe, and they will use all means necessary (Ani) to exile him:
Okonkwo’s immoral actions affect the community. During the funeral rite for the elder Ezeudu, Okonkwo’s gun accidentally explodes, killing Ezeudu’s son. Okonkwo’s crimes enrage the Earth Goddess Ani, for he has consciously and unconsciously chosen death by beating his wife, killing Ikemefuna, and now, killing Ezeudu’s son. His irrational actions are destroying the moral fabric of traditional life. Therefore, Ani banishes Okonkwo to Mbanta, his mother’s village, for seven years.
In short, neither the Earth goddess Ani nor the tribe like to bury one of their own.