Several non-human animal species have been claimed to successfully pass tests indicative of relational matching and to therefore engage in analogical reasoning. Here, we address these claims by focusing on one recent case study. We illustrate several potential methodological limitations that make it uncertain as to whether the subjects in this particular study were indeed showing relational matching. To the extent that similar or analogous limitations apply in other studies, this undermines the claim of relational matching. Apart from this, however, even if relational matching was to be conclusively demonstrated in non-humans, this behavior alone is profoundly different from analogical reasoning as performed by humans. Substantial converging evidence now suggests a critically important difference between humans and nonhumans at the level of behavioral process that explains why nonhumans do not engage in complex language and therefore do not engage in processes that require complex language, including analogy. In accordance with both these arguments, we suggest that caution is needed in the comparative cognition literature when extrapolating from nonhuman to human cognitive capacity.