Arc was pissed at Owyn.
She hadn't really felt the weight of her responsibility with him until "shit hit the fan," as her Father was wont to say. Thus, because she's lost track of him and he'd somehow managed to wander directly into one of the few places she'd told him not to go, she'd had to sit with him for four hours as Amarena interrogated them both.
It was humiliating. It made her feel like a child again and brought back all sorts of bad memories.
By the end of it, she was mad enough that even on the day they were to start at the Academy, Owyn knew to stay well back from her as they walked there with Anko chaperoning them.
So much for being treated as an adult.
After a long, tense walk, Arc and Owyn took their place in the lines to receive their uniforms, and, thankfully, Anko elected to disappear at that point.