Mirai was a huge fan of Toshinori prior to their partnership. He wanted to be of use to his hero and approached Toshinori to be his sidekick. First, the hero refused because of he didn't want to take on sidekicks. However, Mirai was extremely persistent and Toshinori finally accepted him to be his sidekick. From then on, they worked together as a team for five years with Mirai supporting Toshinori with his intellect. Six or seven years before the events of the story, they had a falling out when their values conflicted in regards to Toshinori's injuries.
In that argument, Toshinori was upset that Mirai had used his quirk on him, and felt like his trust was betrayed. However, Mirai only brought it up to protect him, as he saw death in the hero's future. The argument went on until Toshinori left. While speaking about Mirai to his successor, Izuku Midoriya, Toshinori says he specifically can't talk to him because of "personal feelings", but Toshinori mentioned in the manga that "We broke up so it's kinda awkward" in which Present Mic (who had been listening to) points out and mocks him for. Toshinori and his former sidekick finally reunite on his death bed. Toshinori apologizes and Izuku begs him to live. Mirai reveals he doesn't resent either of them and hopes Toshinori can continue to be happy. Mirai reveals that Izuku was able to change the future thanks to everyone's heroic actions. His mind has been changed about Izuku and about how the future can be saved.
Despite his own injuries, Mirio storms into the room in order to speak with Mirai. Crying, Mirio begs his mentor not to die and says he was only able to because of Mirai's teachings that he became so strong. Mirai originally only recruited Mirio in order for him to gain One For All. Before long, Lemillion became his pride. He uses his Quirk one last time to look into Mirio's future. He sees that Mirio will become a finer hero than anyone else. He tells everyone to smile because a society without hope and humor cannot have a bright future. Mirai flatlines and everyone is forced to say goodnight to their beloved Mirai. Mirai speaks to Toshinori about their past together and his hopes for the entire group's future. He states, "All I wanted was for you to be happy" to Mirio and possibly Toshinori as well. Toshinori then begins sobbing and apologizes for what he had said and begs him to keep on living. Unfortunately, Mirai dies soon after.
Fans of this ship like to imagine that the two had been in a relationship during their time partnering together, and the argument they had was a "break-up" between the two.
Particularly, Mirai is normally shown having the deeper feelings towards Toshinori, and Toshinori warms up to him, as their friendship worked in the source material.