Tradition
The most important thing to Koro is tradition. It is far more important than his relationship with his granddaughter and it also blinds him to the fact that she is the obvious leader for the tribe moving forward. In trying to find a way to lead the tribe into the future, tradition in this case actually holds the tribe back. Tradition has it that the leader of the tribe has to be a male. This does not mean that the tribe cannot be led by a woman, it just means that there has not been one yet. Kora fails to see this and his adherence to tribal traditions is to the detriment of both his family relationships and his tribe's future.
There are many references to tradition. The leader of the tribe rides the back of the largest of the whales in the pod. The leader is revealed to be the person who is able to find the whale's tooth thrown into the ocean. There are also traditional fighting and ceremonial tasks that are performed by the traditional leader. At the end of the film it is agreed that it is only by harnessing tradition yet moving with the times and bringing the village together that the tribe will be able to thrive.
Chauvinism
Koro is a chauvinist. He loves his grandchild when she is sweet, little, and malleable, but as she grows up and starts to see the gender inequality of her heritage, and of her present, he becomes increasingly angry with her. He is opposed to her being the leader of the tribe because she is female, but instead of seeing that she is the natural leader he has been looking for, he resents her for performing traditional tasks better than the boys he is trying to mentor. There is a saying that you cannot make a silk purse out of a sow's ear - in other words, you cannot make someone be something they are not. Koro is angry with his granddaughter because he cannot make her into the male twin brother he wishes to, and he is also angry because try as he might he cannot make any of the village boys into a tribal leader.
