It's not that he doesn't like showing his vulnerability to seeing just that he doesn't want to take advantage of it. I love Heejae because of how complex his character is. He's quick to notice that Seyeong shows weakness to those who are pitiful, but the guy is prideful and doesn't want to pretend to gain the pity of someone he likes. Instead, he wants to be loved for who he is, someone with a lot of pride that is cocky at times, headstrong but honest with his feelings (except the whole circus show he did with his revenge plot) and especially, passionate for the things/people he loves.
Though, Seyeong is still my favorite.
It's kinda sad how Heejae does not want to show his vulnerable side to the person he likes