Although things have changed a bit for Isla lately due to her recently obtained powers and Matthew's bestowing of Aline upon her, she still has a habit of depending on him for many things.
Maybe that's not a bad thing, but she's not convinced.
That's why she asked him to let her do several missions on her own. She didn't want to depend on him so much and wanted to regain the independence she once had in the ancient era.
After all, she had lived for 10 million years for a reason. Her mentality, greatly influenced by the time she had spent with the more recent 'Matthew', seemed to want to depend on him, while her old mentality wanted to be part of his strength.
That's why she needed to develop herself and become a sword that he would want to have by his side.
And this was the best opportunity to do so. In this frozen kingdom, where dangers lurk on all sides, she was walking through a large army fighting against her girls.
