What part do you not understand? There's a lot of moving parts.
I believe thats the Problem lol
That's true
Rudger travels and changes his identity often to hide from a particular group in his past and gather pieces of a relic (for an unknown purpose).
He always ends up gaining attention by getting too involved in major incidents even though he is not the hero type.
He just cant ignore injustice, neglect, abuse, etc especially against children!!! (or whomever he considers a child)
In this arc, as Moriarty, he got very angry with the persons who killed Arte and because Casey is an upright person, he would not be able to get his full revenge (aka murder them).
In this chapter, he said the real masterminds would use their wealth and influence to chop off their tail and escape persecution. Casey's lawful ways would slow him down and prevent him from killing them. This risks them restarting the kidnapping and cruelty again. So he decided to play the bad guy to Casey so she would help connect the dots to the series of murders that he was going to commit and maybe reveal as much truth as she possibly can.
On the other hand, Casey always had her doubts as to why Rudger became villainous as Moriarty. Possibly they spent weeks/months together at the university and connected so they more or less knew about each others' character and mannerisms - that's how she recognized him at the Black Dawn hideout some chapters ago. I think in novel, she recognized him from his back because she was used to seeing him from behind in his office in his days as Moriarty (timeline of interaction not shown in manhwa).
She cannot believe in his villainy hence why she invaded his memories to find out what truly happened.
Throughout the plot, just remember: Rudger has a tendency to play the bad guy especially in front of Casey. And he doesnt care for an identity's reputation, he just gives someone else the good name and takes all the blame and hate then migrates again to assume a new identity while searching for the relic.
Who understands the story please explain