Simply put, Half Blood Prince really made me appreciate him and the development his character was undergoing, and I actually sympathized and empathized with him. Draco started out as that schoolyard bully but shifted into really questioning himself and where he stands on following in his father's footsteps, and coming to the realization that he is definitely in way over his head. It continues on into Deathly Hallows, but not as much, though we see his character having been turned from being antagonistic towards Harry to growing up and having a civil understanding between one another in the end. I just find his character fascinating, and I love how JKR really humanizes Draco, particularly in HBP. I'm rather intrigued by the shift with his character and how it shows that he's not really a "villain" as some categorize him to be, just misguided due to his upbringing and suddenly comes to terms with the harsh reality of what it all means. The last two books definitely redefined his character for me, since before that I was going by fanon!Draco.
And I'm not gonna lie, I partially blame the movie!verse for bringing on this love for the character. Tom Felton portrays him so well, particularly in these last two films where he practically stole the show with just his facial expressions showing what he was feeling, and you felt for him. I mean I love Harry as a character, always will because duh, but when it comes to favorites for some reason Draco claims that spot.
Rest of the 30 Days of Harry Potter Challenge.