Eat shit also eat crap means:
Submit to degrading treatment, as in He refused to eat shit from the
coach. James T. Farrell had the one term in Grandeur (1930), They
don't eat nobody's crap, and Mario Puzo the other in Dark Arena
(1955), He'd eaten shit all week.
[The Dictionary of American Slang, Fourth Edition]
In your context, it literally means:
You (yourself) submit to degrading treatment, I won't submit (myself) to any degrading treatment.
which could mean the speaker is not agreeing with the plan the other party suggests because he feels it is degrading and not the right thing to do.
Eat shit is an imperative sentence. It could also mean "no (f***ing) way, over my dead body or f*** you" depending on context. Without any further context, it is not easy to determine what it means. But it is a strong objection to the other party's plan or suggestion.