Human label variation, or annotation disagreement, exists in many natural language processing (NLP) tasks, including natural language inference (NLI). To gain direct evidence of how NLI label variation arises, we build LiveNLI, an English dataset of 1,415 ecologically valid explanations (annotators explain the NLI labels they chose) for 122 MNLI items (at least 10 explanations per item). The LiveNLI explanations confirm that people can systematically vary on their interpretation and highlight within-label variation: annotators sometimes choose the same label for different reasons. This suggests that explanations are crucial for navigating label interpretations in general. We few-shot prompt large language models to generate explanations but the results are inconsistent: they sometimes produces valid and informative explanations, but it also generates implausible ones that do not support the label, highlighting directions for improvement.