The feeling would best be described as a sort of older-sibling protectiveness, but since Terra has never had siblings and sort of wants to protect most people anyway, it's confusing! They have a lot of similarities so it's much easier for her to empathize with him than many people she's met in the City, and she knows how easy it will be for him to fall into pits of depressive uncertainty.

Also he looks like the other her and he likes cockatoos and he indulges her need to dress people up in Amano fashion. What's not to like?