I think Jitae was already seeing his mother in secret that's why on the day his mother was murdered, he was running and at lost. It shows that he knows something about the murder. Since Go Hajoon is closed to his mother (I think Go Hajoon is one of the children Jitae's mother helped just like Mi-Eum), that's why Go Hajoon and Jitae knew each other since they were young. Since Jitae was seeing his mother in secret, he intentionally exchanged their name tag to avoid suspicions when he was seeing his mother
Remember the scar-faced man? Tge secretary of the murderer, I think he was one of the children jitae's mother helped too. Since Jitae's mother was longing for his child, the thing she can only do was helped those poor kids. Ang scar faced man, mi eum , and hajoon were the poor kids. Go Hajoon became an accomplice of the villlain(the one who stabbed Jitae's mother), maybe because he was offered a sum of money and he accepted the offer since his poor and also greediness.
So many people forgot the plot. Yall this is why you reread first remember the long haired guy (real Go Hajoon) said Jitae always switched clothes/name tag with him? They didn’t really explain why yet that I know of…?