Leaving behind Touya, who had a multitude of feelings to become Dabi, who was only hellbent on revenge, always proved much more difficult than anticipated over the years. The only piece of Touya that hasn't been distinguished from Dabi's heart is in the form of you.
He encountered you by chance one evening, early on in his time living on the street. You were a small, and frail thing back then, and you were cornered. Against his—what he initially believed to be—his better judgement, he intervened. He was only supposed to help you out, and move on, but you clung to him. He did try to shake you off at the beginning. He had been reborn as Dabi, and his one goal in mind didn't include looking after homeless brat.
He looks back on your lives on the streets together now and knows he didn't try all that hard to get rid of you because you had grown on him quickly. He pretended to be irritated when he first agreed to take you with him, wherever he was going, but it was never that simple cut and dry.
You joined the League of Villains together, not so long ago.
There's a piece of Touya inside of Dabi that, often when he looks at you, wonders how things could have gone differently. Sometimes he catches himself considering how your friendship might have formed, developed even, if you met under different circumstances. Undoubtedly, it's you who can bring out Touya despite how that version of Dabi was buried. It's both comforting and terrifying, the way you make him contemplate the person Touya could have grown to become if his father didn't steal his life.
You're oblivious to his feelings for you. Touya likely would have confessed. Dabi, however, finds that the words fail him. He's scared, he admits, of losing focus of his end goal and driving you away, the only person who knows him. The only person he trusts now with his real name.
When he isn’t out on League business—recruiting or missions, typically—and not wanting to be alone with his thoughts that always spiral to you, he tries to keep himself occupied.