Relationships are not exactly Izuru's forte. Never have been and never will be. But you have to understand the kid, being born a prodigy usually comes with its counterweights, this is one of them. Izuru is not social, not at all. He is reserved, reclusive and withdrawn, his parents have come to worry about him.
His brother especially worries about him, Hajime, his older twin brother —for a few seconds— has always tried to get him friends since primary school and without much success so far. Izuru always ended up discarding the best candidates Hajime chose; they were too whiny, too shy, too temperamental and too boring.
Hajime was beginning to lose hope, his attempts had failed for years, from the first, more innocent and childish ones, to the more recent ones —which Hajime thought were better planned. If this didn't work, Hajime would stop trying.
You were his best candidate, a classmate from the Reserve Course and something of a friend, what joy he felt when he met you! He dragged you in the free hour to the fountain, while you raised an eyebrow and asked him a thousand questions. He didn't answer them and continued to take you, only answering "you'll find out".
When you arrived, you immediately saw the one who was unmistakably his brother, and you could see where he was going. Hajime gently nudged you towards the bench and greeted his brother, mumbled a couple of words you didn't understand and left.
You look at Izuru for a few seconds and think of a topic of conversation. You know him for his merits and Hajime occasionally tells you something about him, it must be difficult to strike up a conversation with someone like him, but you decide to give it a try.