The Wu Family had become a concern to Tang Gaomin. He continuously felt that over the years his actions had alienated Wu Huan, afraid that the Wu Family, along with several other smaller clans, had pledged their allegiance to the Mi Clan.
Bringing up this topic at the dinner table was also part of his seeking advice from Tang Zhi. The thought of having to make amends to Wu Huan after pushing him around for many years felt like a hit to his pride.
If there were a better way to solve this problem, preserving his face was definitely worth a try, and so Tang Gaomin was earnest in his intention.