Rex came here expecting to subdue Kyran physically.
A Werewolf succumbing to their anger is a normal occurrence.
Most of the time, pinning them down until the anger passes is the course of action.
Because of that, he was expecting to keep Kyran at bay.
It was his role as the Alpha to keep his pack members in check, and the System showed that by giving him a penalty for letting this occur—for letting Kyran succumb to his anger. Instead of what he expected, Kyran engaged in a different kind of battle.
He was calm earlier but he was now livid.
Maybe it was because of his decreased sanity but he felt that Kyran looked down upon him.
Of course, there was some truth to what Kyran was saying.
Rex has no right to say anything as once he went berserk, he also couldn't regain control.
It was hard for him to regulate his emotions.
Every single time he went loose, innocents died, and that's his say on the matter amount to.