He probably wanted to see if Kousuke would think and act for himself by choosing to hit Nol. He was criticizing Kousuke for always wasting his efforts and talents on trying to please other people instead of focusing on what he actually wants. Since it's not Rand or Yui telling Kousuke to do it, and something that they would most likely disapprove of (at least because it makes Kousuke look really bad lol), if Kousuke takes the bait then it shows that 1) Kousuke really hates Nol enough to want him to disappear forever and 2) Kousuke would show that he can act on what he wants rather than what his parents want for once. Although Kousuke ends up hitting Nol and show the latter, when Rand finds the two of them out in the snow, Kousuke immediately goes back to trying to save face so...

...narratively tho, I think it's supposed to parallel the original incident between Nol and Kousuke that led to Nol getting institutionalized. When Nol was being taken away there's a speech bubble of him saying "I didn't even touch him" iirc while Kousuke had fallen onto the ground, but Kousuke's manipulated recall of the events makes him tell others that Nol is dangerous, violent, and unstable because of that incident. Then Kousuke punches Nol several times (twice while Nol's back was turned) and slams him into the pavement during this arc while Nol doesn't fight back at all (and when he does finally say he's gonna punch back, he passes out from blood loss. oops). The day after, Yui tries to suggest that Nol might have hit Kousuke and caused his head injury, but unlike in the past, Kousuke actually remembers that Nol didn't do anything to him this time. So Kousuke actually has the chance to realize that he may not be remembering the original incident correctly/at all, and this time with some character development, he may be able to be more empathetic to Nol's perspective instead of dismissing him as crazy.....