I enjoy reading this manga for two main reasons, 1) It's wonderfully atmospheric in the way that it combines fairies/fae/supernatural ideas, and 2) I'm always pleasantly surprised by the way in which the title is character- and relationship-driven.
There's a particular page that bluntly describes how mages is in this setting often take apprentices, and that the master-apprentice relationship is similar to a parent-child relationship, but that it isn't unusual for this relationship to become a spouse-spouse relationship. Understandably, part of me balks at that thought, because I hate the power imbalance in a teacher-student relationship, so it seems kind of shady when those relationships become romantic. Similarly, I found this series kind of suspect because Elias literally buys the Chise, and she seems more like a trophy or prisoner (hello, Stockholm Syndrome). However, Kore Yamazaki somehow manages to make these things seem less creepy because they way that she develops the characters and their relationships rings true. When I was reading this, I thought that the characters and relationships aren't necessariliy "realistic," but then I was reminded of the major shonen-ai work Heart of Thomas, and how the characters weren't necessarily supposed to realistically reflect people in society, but rather be constructs to explore human interactions and feelings beyond conventional (in that case, gender) roles. I think that The Ancient Magus' Bride does something similar between two characters. They're not necessarily human or have easily-describable life experiences, so they have the freedom to be flexible characters who help the creator explore emotions and relationships.
I also enjoyed that Chise was basically told not to be so passive. A common story is a bland main character suddenly becoming awesome despite being pathetic at the beginning of the story. I enjoy how this series is a slow burn and actually shows Chise coming into herself over time. In the same vein, I enjoy how the relationship between Chise and Elias grows over time, and how it is increasingly being portrayed as bidirectional, and the characters are beginning to think of it as a *mutual* give and take, rather than Elias merely being Chise's guardian, teacher, and benefactor.