--- Based on my first impression I'd have to say, he said, throwing in a dramatic pause, I hate you.
and then, a few beats later...
--- Akiko was not one to take insults lying down, however, and snapped out of her fit of embarrassment.
I can't see anything that she would have been reacting to except for Kakashi's line. If she was reacting to Kkashi's line, you're certainly heavily implyings that it's an insult. If you just say "such things" rather than "insults", it dodges that. There are better fixes, but I'm not running on enough cylendars to come up with them right now.
and then, a few beats later...
--- Akiko was not one to take insults lying down, however, and snapped out of her fit of embarrassment.
I can't see anything that she would have been reacting to except for Kakashi's line. If she was reacting to Kkashi's line, you're certainly heavily implyings that it's an insult. If you just say "such things" rather than "insults", it dodges that. There are better fixes, but I'm not running on enough cylendars to come up with them right now.