Kenai had absolutely no reason to kill the bear

Just think about it. If you truly think about it, Kenai had absolutely no reason to actually kill the bear! His main reason to kill Koda`s mother was to avenge Sitka, blaming her of "killing his brother". Before it`s release, it was announced by various sites that Kenai would avenge his brother by killing the bear who killed his brother. But Koda`s mom never actually killed Sitka! It was Sitka who sacrificed himself in order to save his two brothers from the bear. And all because of Kenai`s stupidity!
And what`s worse was that everything was Kenai`s fault! It was Kenai who had forgotten to tie the basket up. And when he went to retrieve it, it was he who deliberately harassed the bear by throwing rocks at her. If it wasn`t for Kenai`s foolishness, both Sitka and Koda`s mother would`ve still been alive. Which means that Kenai killed a poor, innocent bear for no reason whatsoever! If the bear had actually murdered his brother, it would`ve justified Kenai`s actions more.