It didn't surprise Kay that John said he didn't want her getting involved in in his plan, especially after the night before and how that situation turned out. Truth was, she actually didn't want to protest him on the matter and felt more than okay in not going. She didn't however like the fact John was planning on going alone, and was thankful that Bane said something about it. 

Fia also didn't like the plan, folding her arms over her chest, she stared right at John. "I'm going with you. Bane is right, no way are you going alone. You're going to need someone to watch your back whilst you do this and right now I'm the next most powerful one awake and with it enough to be of any help" she pointed out. She also partly and selfishly wanted to be with her dad of her past on her own without anyone else around.