WARNING: The following contains spoilers for The Irregular at Magic High School, "Reminiscence Arc," now streaming on Funimation and Crunchyroll.
The Irregular at Magic High School takes place in a world with an alternate history in which magic exists. Following a third world war that lasted 20 years and decimated huge chunks of the human population, the planet was divided into four major superpowers with Japan being one of the four. As a nation, Japan is governed by Ten Master Clans, one being the Yotsuba Clan, which co-protagonist Miyuki Shiba is set to lead in the future.
Much of The Irregular at Magic High School focuses on Miyuki's relationship with her older brother Tatsuya, who is also her bodyguard. The "Reminiscence Arc" takes a break from the present timeline to explore the origins of the two siblings three years before the Season 1's "Enrollment Arc". While Miyuki is very strongly attached to Tatsuya in the present, the "Renaissance Arc" reveals this wasn’t always the case.
Before becoming aware of her brother's powers and magical talents, Miyuki didn't think highly of Tatsuya and treated him like a servant, much like their mother and the rest of the Yotsuba Clan did. While Miyuki wasn't cruel toward him, she wasn't affectionate either; she just left him alone to carry out his duties as a family servant. What she did take issue with was having him accompany her everywhere she went -- because he creeped her out. This was most notable during a family trip to Okinawa in which she wanted to go out for a walk to enjoy the nice scenery.
Tatsuya stayed behind Miyuki during her walk, which made her feel uncomfortable. At first it seemed like her discomfort was coming from a place of scorn, but it quickly turned out to be different. Miyuki found herself questioning why her older brother wasn't afforded the same level of respect as the rest of the Yotsuba clan. She also didn't understand why she was questioning this, since she'd been brought up to not think of Tatsuya as an older brother or address him as such.
It wasn't until they ran into some Left-Bloods -- soldiers who are descendants of American soldiers post-World War III -- during her walk that she started to see Tatsuya for who he really is. Finding the soldier, Joe Higashi, to be a threat to Miyuki, Tatsuya quickly intervened and engaged him in hand-to-hand combat, winning easily. This was enough to impress Miyuki, only adding to her conflicting feelings toward her brother.
As Irregular's "Reminiscence Arc" goes on, Miyuki finds herself feeling compassion for her brother, which quickly escalates into feelings of love. Despite her newfound feelings, she struggles to understand why he only feels a sense of duty to her and nothing else. This confusion especially comes through when she tries to prop him up to her mother's bodyguard, Honami Sakurai. When he dismisses his own protection of Miyuki as nothing more than doing his job, she feels a little hurt.
During a conversation with Honami, Miyuki learns that as the heir to the Yotsuba Clan, she must get used to not wearing her emotions on her sleeve, as it can make her vulnerable to the wrong people and compromise her position within the Clan. Despite this sound advice, Miyuki still can't help but feel a little jealous of others interacting with Tatsuya at her cousin Mitsugu Kuroba's dinner party, especially when she sees him genuinely smile -- something he never does for her.
On the eve of the Great Asian Union's attack on Okinawa, Miyuki, her mother and Honami are all gunned down by infiltrators at the Onna Base. They are only saved when Tatsuya resurrects all three of them and kills the infiltrators. Since protecting Miyuki's life is Tatsuya's responsibility, he accompanies the Onna Base soldiers to fend off the Great Asian Union as payback for harming his sister. These actions are what ultimately solidify Miyuki's love for Tatsuya to the point of inquiring their mother about why he feels a sense of duty to her.
The siblings' mother, Miya, reveals that after performing surgery on him to augment his magic abilities, one of the side effects resulted in the loss of his emotions, all except for one: love for his sister. From that point on and into the present-day Irregular at Magic High School, Miyuki commits herself to her brother -- even if she knows she can't be with him romantically due to blood relation.