[Arthur knows by now that if he got a letter from their father asking him to drop out of school and come home to a normal life, then so has Morgana. And he also knows that Morgana is much less likely to take it quietly. It wasn't as though Arthur enjoyed the letters or agreed with what was written there but he wasn't the sibling with the temper.
So maybe he's waiting outside of her last class to catch her, just to see how she's doing. Because he worries about you, you stubborn woman.]