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Background. Large Language Models (LLMs) have demonstrated strong performance across a variety of code-understanding tasks, leading many to believe that they can reason about program semantics. A fundamental test of this capability is assessing code functional equivalence. However, existing evaluations primarily focus on single-language settings or rely on synthetically generated code, raising concerns about whether current results reflect true semantic understanding. Aims. We investigate whether LLMs can accurately judge functional equivalence across different programming languages in human-written code, a setting that requires deeper reasoning beyond superficial similarity. Method. We introduce PolyHuman, a dataset of human-written programs in CPP, Java, and Python. Using this dataset, we evaluate intra- and inter-language equivalence detection across open-weight and proprietary LLMs, selecting GPT-o4-mini as a representative model to assess stability. We then manually analyze 81 cases of systematic disagreement in which models incorrectly judge functional equivalence, examining the code logic and the generated Chain-of-Thought reasoning. Finally, we categorize these failures and compare them across GPT-o4-mini, Claude-Opus-4.7, and Gemini-3-Flash to determine whether they reflect model-specific issues or broader limitations of state-of-the-art LLMs. Results. We identify a difficulty-dependent breakdown in equivalence judgment (harder problems make the model increasingly prone to misclassifying non-equivalent code as equivalent), a model-specific sensitivity to programming language for the best-performing model (particularly a more conservative behavior on Python), and a partial reliance on similarity-based cues. GPT-o4-mini also shows substantial run-to-run instability under identical settings, indicating inconsistent rather than absent capability. Its failures are mainly due to (1) a lack of knowledge relevant to judging code functional equivalence and (2) abstraction-level reasoning failure, such as premature conclusion, semantic-level misunderstanding, and implementation-level error. We also observed that several analyzed failures involved loops and conditional branches. Conclusions. Current LLMs do not reliably capture functional equivalence within or across languages. Our findings highlight the need for more realistic benchmarks and suggest improvements through better reasoning-path selection and by addressing reasoning gaps across the identified failure levels.