He is so sincere! That may be what I love most. He will not be deceitful with the Volturi even when they are literally lying to him. He does not try to control his family. He plays with them!
He wants a companion so badly but agonizes over changing Edward. The idea of his "fathering" Edward and teaching him about being a vampire and the life he will face makes me just love Carlisle! I see Carlisle and Edward as having an unbreakable bond, special beyond Carlisle's relationship with the other family members. When Edward asks in NM, "Why are you doing this to me,?" they both seem to struggle so much but have to be honest.
Carlisle is pratically perfect in every way!