It's because he has always felt so guilty that when his dad sat them down with the pictures he was too afraid to speak up for Han-Gun and defend him or even say that he was an important person to him. So he looked at this as an opportunity to finally stand up and do what he should have done then and say that Han-Gun wasn't just some random acquaintance but someone he loved. Even if they ended up never seeing each other again after this he felt he owed that to him.

I love this story so much but I found it kinda funny where instead of the casual yea I know him Won said yea he’s not just no one but someone I loved. LMAOOO so extra and it was so dramatic cause like who asked. But still cute nonetheless