(MAJOR SPOILERS AHEAD!! DON’T READ UNLESS YOU’VE FINISHED “Bastard”)
Dongsoo has a criteria for the women he kills. He kills women that look like his wife. I believe he does this because of the love he holds for Jin. When Jin was young, he discovered his Dad’s secret hobby. However, Dongsoo, in his insanity, enjoyed this time even calling that “time alone the greatest moments with my beloved son”. Dongsoo connected to his son and saw himself in Jin. This is why Dongsoo is constantly telling Jin that he is the same as him. This connection with his son ended up heightening his anger and delusion when Jin’s mom attempted to kill Jin. From there on out, Dongsoo began killing women that looked like his wife to satisfy his anger and also to prevent him from people like her.
After Jin confessed his love for Kyun to his Dad, He wasn’t accepting at first telling Jin that first loves always pass probably because Kyun reminded him of his wife and his trauma made him want to protect Jin from people like his wife. Also cause he’s a psycho and wanted to kill her lol. Dongsoo then immediately started testing Kyun after he figures out that Jin’s “a man” :). He did this because he knew Jin wasn’t bluffing but he wanted to make sure she was the one. He never intended to kill her because he didn’t yet know her true nature. Therefore, Jin was ultimately protecting her from nothing throughout the majority of the WEBTOON. Dongsoo even admitted that he was testing Kyun and that she passed: “She’s a reliable girl, worthy of leaving my only son to.” Dongsoo kept on targeting Kyun and exposed Jin attempting to murder Ms. Kim to her (the Chinese lady), to make sure that Kyun would accept Jin for who he is (a murderer). Jin’s Mom didn't accept Jin for being a murderer and tried to kill Jin and Dongsoo didn’t want that to happen again. He was just trying to keep Jin safe and make sure Kyun wouldn't try to hurt/kill. He knew she would most likely find out he was an accomplice eventually.
You may be still convinced that Dongsoo was using his classic lying and manipulation tactics to just to mess with Jin psychologically. I don’t blame you, however, he had no reason to. Dongsoo’s reasons for lying have usually been to either save himself or to manipulate and kill others. He did neither of these things during he and Jin’s final interaction. He let Jin go with Kyun, whom he never harmed, he never even drew her blood. So he didn’t want to kill Kyun or manipulate Jin. He kept his word: “If Kyun understands the way you are and keeps loving you, then it’s a complete victory for you. As for saving himself... we all know how that ended. The last slide of the WEBTOON shows Dongsoo’s mangled corpse on the concrete, still clenching the painting titled ‘A father and his son....A symbol of his twisted love for Jin...