I'm a little  bit confused on this matter. At first I thought Im Hyungtaek and the mom who was killed are his parents, but then when Seoktae came to visit the mom at the hospital, he said Hwayi seeing monsters must've been a trait he got from him. 

The real parents are definitely In Hyungtaek and his wife. This is evident by the posters and decoration kept in the top part of their house, and the heart-wrenching scene when Hwayi found his mom (the one in the hospital) got murdered. Seoktae said that he got the trait from him isn't biological, rather raised, or simply relatable. Seoktae has experienced that condition, which is caused by PTSD, and he thinks he could therefore 'cure' Hwayi of it. 
basically what @skyryle wrote. 

I think hwayi’s dad is seoktae... because in the past seoktae purposely rape hwayi’s mom

 funnysimba:

I think hwayi’s dad is seoktae... because in the past seoktae purposely rape hwayi’s mom

My view exactly.   Seoktae raped hwayi's mother ( In Hyungtaek's wife)  when they were young because he hated everything about  In Hyungtaek. She must have had a baby.      

 LKSR:

Seoktae.

agree

I belive that Seok Tae is his parent(bc he raped the girl that was in love with HyungTaek that  can be the HT actual wife).