I still don’t understand why she has to pretend she’s not Ayrin. No matter how much I ...

First, her reason is she didn't want to die with her first meeting with him that's why she lied. Second, it is because she wants the ml to accept that she's dead already, move on, and be happy like falling in love with other person. Ayrin doesn't want ml to be stuck in the past. And I guess she's doing that in a wrong way hahahaha cuz the ml probably already sense she's Ayrin.