Dan-Han badly wanted to tell Eun-sun that he wasn't just suspicious about who her parents were, but that he was almost certain of their identity. But despite how much he wanted to tell her, he knew he couldn't. And this wasn't because he was afraid he might be wrong, but rather because, knowing would put her in danger.
If the person who had given her to Song-Hee wanted to get rid of her as a child, then nothing was going to stop him now when he finds out about her existence. That alone was already an issue of concern in his mind.
Was he not concerned about her existence? Or was there a laid out plan that kept him at ease?
Dan-Han didn't know what to think of the situation. He must have deemed her a non-existent threat for him to have kept her alive, else he'd have had her handled all these years. This negligence or non-chalance, whichever it was, was favourable to him and must be what have kept Eun-sun alive for so long.