Of all of Carol's decisions in the past, this is the clearest one, even if I think the show didn't handle it correctly.
She clearly spelled it on the letter, to both: If she stays, she will be
forced to remain in the "mother" role (ie, having to keep killing, to protect those dear). She can't just say no, while remaining there. She will have to. Endlessly. Having a family means having such responsibility weighted on her, because she has such skills. And being in a community means resources, which makes them automatically a painted target.
Her leaving, means that from now on, it's all on her. Sure, she will still find enemies (like in this chapter). But without an anchor, she suddenly has options (
the opposite of when she and Maggie was captured -- she had to act, for her sake). She can more easily avoid confrontation. She can freely travel, join other camps and then leave. She can give up and let herself killed or go full Rambo. Her fate it's now under her terms.
It's arguable if that's a better way to live or not. But the notion behind it is not hard to grasp. And while the show has not fully bring the idea yet, it might also be a journey about getting in peace with herself (ie, preparing to die).
Extra: She is traveling the opposite side where the Savior base was. That's why the chapter was called East. She is trying to leave that life behind. Unfortunately, it's not that simple.
Then there's what he did to Otis during the medical supply run. Lying about the hostage taking his gun.
Wonder what today's Rick would do, if he were in the same scenario than Shane (injured, carrying an unfamiliar "weakling", his son's life at stake).
Being injured and without weapons means that he can't unleash judgement-day mode. So, what would he do?