Eating the elephant
Some analogies are even more useful if you unpack them a bit more. For example, here is my take on eating the elephant:
Sure you can eat an elephant one bite at a time but sooner or later you are still left with a huge carcass you need to heave into a skip [dumpster].
We were talking about this in the context of transforming a legacy environment using the Strangler pattern.
Sure you can improve a legacy horse to be a more nimble horse and maybe even teach it to tap dance. But you can't gradually turn a horse into a unicorn (Mixed metaphor championship entry).
At some point you reach the limit of what can be bitten off (back to the elephant metaphor - don't bite horses), and at the heart of your systems lies a tangled mess of inedible inseperable legacy systems. .
Sooner or later a major exercise is still required to replace the bulk of your problem, to throw away the inedible carcass of the elephant and start anew.