My theory is that Yuhon believes if he becomes king, it will save Yonhi from the curse of her blood (guessing he finds out when she started getting sick). I'm also guessing King Il finds out about her heritage at some point (through friendly means, I'm betting Yonhi and Il become friendly enough for her to tell him or something) and that's why King Il didn't want Yoona to marry Soowon. He didn't want her child to have the sickness down the line.