As for my personal take on how the manhwa is playing out so far, I don't think Guwon is a liar. He’s actually honest because he just doesn't see a reason to lie. He’s a total narcissist who thinks he’s above everyone else, and he views everyone around him as just dogs and followers.
When he started treating Jinwoo differently as they grew closer, it was because he saw Teach as someone just like him—someone special, different from the rest, who mirrors himself. So in his head, whatever he does is right, and it's the absolute truth, which means he feels zero need to apologize or lie about it.
And regarding the whole thing with Teach's dad, I don’t think he’s lying about that either. I honestly don't believe he actually killed his dad. He definitely knows what happened and how things went down before that, but he's probably withholding the full truth because Teach mentioned before that he wants to remember everything, no matter how painful it gets.

Wait did Guwon kill the child or did he let him go ? I forgot how violent this story actually is for a sec there