
The old man on chapter 2 is the same person at the beginning of chapter 1 who killed his omega partner because apparently the omega found their "mate". On chapter 1 he says that he is an alpha and he says it again when he is seen talking with Eren on chapter 2. As Aeriesky21 pointed out, we don't see or know who is Levi's mate.

ohhh okay i thought that maybe armin might have been his mate but that didnt make sence coz they call armin a beta more than once.
also i think that old man is likely a parent figure or a guardian to levi, or was, there was something levi said to the doctor about erin that made it sound like he was scared to turn out like the old man (killing his lover coz they found there mate)
Was Levi's mate the old man?