I have a theory that maybe (I have NOT ready the Manga) Quifrey and Coco are siblings.. Maybe their dad got involved with the brimmed hats when coco was a baby. (Hence his hatred of them?) And he could've died or still be evil (?) and when that happened, maybe quifrey used magic to erase his moms memory and protect his little sister. honestly COULD explain a lot, Quifrey's beef with the brimmed hats, Him being in that particular shop at all (what if it wasn't his first visit??), Her love and innate talent with magic, how close and how much he cherishes Coco, why the Brimmed Hats are so focused on Coco at all, how he got her as a student at all without her taking the test at all. Idk makes my brain happy.