I think it is a little bit strange too but I have only added styrene, dichloromethane and AlCl3 as the reagents. So CH2Cl2 should be the reagent to form a cationic species for the polymerization.
In addition, the experiment said it is a cationic polymerization of styrene and if CH3Cl is used, the mechanism is sensible.
But I am not pretty sure how CH2Cl2 can form a cation with AlCl3.