In the Torah Portion of Pinchas, Pinchas' ancestry tracing back to Aaron is mentioned. This, according to Rashi, is to point out that the trait that Pinchas used when he killed Zimri and Kozbi was that of Aaron, his grandfather, and not the influence of his non-Jewish ancestors on his maternal family tree.
Based on a talk by Rabbi Yissoscher Frand
The idea that Pinchas' inherited traits that he got from Aaron seems strange. Aaron was called "The lover of peace, the pursuer of peace." For instance, Aaron was famous for bringing families that were on the verge of divorce back together. What sense does it make to point out that Pinchas got the inclination to kill two people from an ancestry that was so famous for peace?
The Chasam Sofer makes a fascinating point. The words "pursuing peace" can be interpreted literally, as if one is chasing peace away. There are times when it is appropriate that we stand up to a situation that is wrong and based on empty values when we should not peacefully stand by and let things happen. When Zimri and Kozbi committed immorality in public, this was a perfect situation for someone to "pursue peace," to chase away the inclination to stand by and watch a bad thing happen peacefully. This was Pinchas, who remembered the law and ran and killed Zimri and Kozbi and saved the Jewish people from being wiped out by G-d's Anger.