After all, as a giant figure in the Demonic Way, the Purgatory Demon Monarch is an enemy to many across the world. Even if his circumstances are somewhat better than his adversary, they are not much better. Once he shows a point of weakness, enemies will attack him as well. That is why he is unwilling to fight directly with the Purgatory Demon Monarch unless he is entirely confident.
But now, this concerns the Great Refining Technique and his own hopes of becoming a Taoist Monarch. Especially given the attitude expressed by the Purgatory Demon Monarch at this moment, who is also after the Great Refining Technique, it means there is no room for retreat. He absolutely cannot avoid or shrink back anymore.
"Indeed, becoming a Taoist Monarch has never been smooth sailing. Without defeating countless opponents, one is not qualified to become a Taoist Monarch." The Ten Thousand Beasts Demon Monarch thought to himself.