When Izumi is emotionally devastated over being told that he has no talent for the manga industry, Ryouma personally goes to Saotome with Izumi's manuscript and has him review it. Even better, he wrote an inspirational message to Izumi encouraging him to keep pursuing his dream. He even drew Lala-Lulu herself telling Izumi that she's rooting for him.
The mere fact that Rei stayed awake for two nights awaiting a message or a call from Izumi. He knew that he must have hurt Izumi's confidence when he told him that his manga was awful and he wanted to apologize to him. The moment that Izumi arrived home, he hugged him and shed tears of joy.
Rei has another moment in the tenth episode when he tracks Izumi's location. Rather than tell Shougo where Izumi was, he responds by distracting Shougo by asking him to come over for a drink after work. He knows very well how overprotective Izumi's brother is and he was giving Izumi and Ryouma a chance to be alone together.