Cuckoo eggs and great reed warbler eggs look alike, and the question asks which relationship between the two birds would actually cause that kind of egg mimicry to evolve.
Only the brood parasite relationship creates a real selective pressure for egg mimicry: the cuckoo's reproductive success depends on the host failing to notice the foreign egg, so cuckoo eggs are pushed toward looking like the host's own eggs generation after generation.
Let's summarize:
So the similarity in egg appearance is explained by the common cuckoo being a brood parasite of the great reed warbler.