"Because I AM Joel."
Then you are also dead.
There better be more to story than this. Abby needs to have bigger goals and ambitions beyond just killing Joel. I'm not super confident this will be the case, there's still the fact that her link to the main characters is an extremely thin and lazy excuse for this game's existence. Using their logic:
Last of Us Part 3 - Turns out a random no name Abby killed on her revenge quest has a cousin named Tom. We never saw or heard of him, but now he's out to get revenge on Abby.
Last of Us Part 4 - Turns out a random no name Tom killed on his revenge quest has a grandma named Joan. We never saw or heard of her, but now she's out to get revenge on Tom.