@Lovelyspacepanda
Okay, this is my own interpretation since I only understand part of the raws for the later half of season one so take it with a grain of salt.
Bin does care about his son but as a hundred-something vampire, he’s so used to people dying on him that while he cares for Hwa, he’s not too desperate to keep him from danger. The contrast between vampires and lycans is that vampires are detached due to their immortality while lycans care a lot for their family. Plus Hwa is similar to Bin in personality so Bin is probably like “He can take care of his own problems.”
Gok, on the other hand, is very caring and emotional so Bin often play along to keep him happy.