"As for how I'm going to handle the background and so, I already planned to deal with his father. So, we can just say that this is called preponing the plans that I previously had." Jack stated with his eyes turning cold.
Since it seems that he had to deal with Arthur's father as early as now, then Jack won't shy away from this opportunity or challenge. Jonathan had already ruined his plans to meet with the Jesda family only after he was sure that he could destroy them as long as they tried messing with him.
Although he didn't mind being confused with Jonathan as long as the confusion wouldn't need him into problems, he was quite tired of it. If the members of the Jesda family could know that he and Jonathan were lookalikes, then it would be make things better for him.