Responses
Based on what was given to us, it seems Seol-hyung's mom wasn't married to the dad when they had him. Maybe their parents didn't approve or maybe she didn't want to because of her illness??. I wish the author had given us a little more there.
But it was clarified that Seomoon-hyung's mom and the father got married before they had him

Wait… I’m confusion, someone help me out here if I’m wrong, but… his brother isn’t born out of wedlock, right? He was born from his father’s first marriage, but then she died and then their father remarried. Or was the father just dating his first born’s mother and that was how he was ‘born out of wedlock’??