Harkam had scoffed at the request to apologize. He felt it was harmless. He also didn't want to apologize because it will weaken his image as the new grand god. That's how their conflict started. First, it was the little things but it escalated when Stelios killed Pitran when the demigod failed his challenge.
Harkam doesn't care about Pitran just like he doesn't care about Tyke. He cares more about what the existence of Pitran meant to him. For a god to shift to the path of perfection, they need to attend the trial of heaven. But a god can't leave the plane as mortals can. The only way for them to leave is when a channel leading to the tower of heaven opens in the divine realm before the trial.