>>282205222
At first no one believed she would be executed. Then as the truth dawns on them their resolves start wavering. Byakuya is basically hollow until Ichigo beats him. Losing to Ichigo ironically took a massive weight off of Byakuya's shoulders. It shows in his gratitude in later arcs.
Truly a commoner such as yourself could never understand the responsibility a nobleman like him feels to set a good example for society. The law hurts but we have to follow it for the sake of peace and prosperity.