Green’s Dictionary of Slang

crawfish v.

[SE crawfish, the US synon. for crayfish, a lobster-like crustacean. The term echoes the characteristic backward movement of the fish]
[mid-19C+] (Aus./N.Z./US)

1. (also crayfish) in fig. use, to back down, to renege on a previous statement, commitment (the image of is of personal humiliation).

2. in lit. use, to move backwards, to retreat, to run away.