Arad's current goal was to survive the clash, not win it. He wasn't strong enough to face either Yog or Amaterasu, and since Cain could challenge them both, he was certain that he couldn't face him either. But he was strong enough to understand their intentions from the pulses of magic surging through the air.
The assailant, Cain Lisworth, had a goal to capture Yog. His magic and expansion surrounded her magic and tried to seal her away. It was clear that he wanted to capture her alive. Arad could almost wish him luck since Yog isn't the kind of woman to be captured so easily.
Yog's intentions were similar to Cain's, and probably even more sinister. She didn't try to capture him directly, but instead wanted to infect him with her forbidden knowledge and control him that way. This entire clash was just a massive tug of war between Cain and Yog as each tried to dominate the other.
