I think it’s important to acknowledge the fear in Emma’s expression because for the first time in a long time, someone’s looking at her, wanting to understand her as a child who’s given a kaleidoscope for the first time. There’s nothing more captivating, inviting, gorgeous, or inspiring. Despite being able to read her as a mirror image of himself, he values her to a much higher extent and understands that her beauty can be explored further. He can see how hard this journey’s been for her, and yet he’s proud of her. He’s proud of her for taking charge and fighting. He’s proud of her for confronting what he knows must’ve been difficult. Since Emma understands him, she can see the heartfelt desire in his expression and that frightens her because she doesn’t want the past to be repeated. She doesn’t want to let someone in so she immediately walks away when she realizes how truthful he’s being. If there wasn’t a part of Emma that had wondered what being adored by him would be like, she wouldn’t be afraid of his desire to get to know her. The feeling is so incredibly unfamiliar that she’s afraid of exploring it because of how much her past has damaged her.
Essentially, not only does he want to learn the details of her soul in depth to patch up the wounds for good, but he wants to understand them in order to ardently love every part of her.