True, but I kinda get it. He's Nux and being in touch with his adoptive son can be seen as weakness by others. They'll be both targeted and since he's new, it's better to separate for the mean time and when he gains power and establish himself as a powerful Nux then they can peacefully reunite.
Doyoon could become a target for other people if they knew he was Jooyoung's adoptive son. I think it was the right choice that Jooyoung left him, but sad nonetheless. He's better off proving his power to other vampires first before going back to meet Doyoon again.
Where is Nux going that he won't be able to keep in touch with his adoptive son? Can't they both just get cellphones? Lol