In "Lyra's Magnum Opus", Sana's best friend Yami HATES Tetsu from the start. We find out that he's hated Tetsu for about fifteen years due to general distrust, jealousy of Sana's affection for him, and worry that Sana will become attached to others who will be bad for him. Tetsu becomes the symbol of Yami's worry about Sana meeting people who might put him in danger when he can't defend himself due to his illness. Sana is also Yami's only friend, due to Yami's extremely abrasive personality (that he's not aware of), so Yami is fiercely protective of the only person who loves him and gave him a chance. Eventually, Sana and Tetsu fall in love many years after Sana developed this crush. Tetsu does not understand Yami's hate at first, and he's too preoccupied with Sana's worsening illness to really pay attention much. Over the course of eight books, the two become very good friends and understand each other well. It's definitely a journey, and a beautiful one to see. You will cry. They become co-caretakers of Sana, who is slowly dying from his terminal illness. By the time they are in their 60's, Yami and Tetsu are such good, lifelong friends, that Yami becomes the caretaker of Tetsu (as per the epilogue).
Writing relationships that evolve from dislike takes nuance. It takes a long time to work out based on the particular characters' biases and reasoning. You have to make them appear sympathetic eventually to the reader after a long time of often intense hate. It can be hard to get right. Making it feel natural involves making the characters feel real and like something your friend or even you might do or how you or someone you know would react, no matter how immature. Real people are immature and unreasonable. Your characters can be, too.
Writing Tetsu and Yami's friend relationship took a long time, a very long evolution due to the reasoning for Yami's hate. He's also an abrasive person in general, and disliked by most of the other characters except for Sana who'd defend him to the death. Due to this love from Sana, it made Tetsu start to question why Sana defended Yami so much and stuck by him. There must be something good inside him for Sana to love him for all these years. This was he seed that started the evolution.