Let $C_*$ be a complex non-zero from $C_{-1}$. Let $C'_*$ be another complex non-zero from $C'_{-1}$. Suppose $C_*$ is a projective complex over $C_{-1}$ and $C'_*$ is an acyclic complex over $C'_{-1}$. Let $f_{-1}:C_{-1}\to C'_{-1}$. This induces maps on $h_*:C_* \to C'_*$ on complex level. It is not hard to show that any such $h$'s are homotopic.
What is the intuitive explanation that all such $h$ are homotopic? Knowing the conclusion to prove is easy. This conclusion is not natural for me. I cannot see at the first sight that any $h$'s are homotopic when I see the assumptions.