Recent calls for pluralistic alignment emphasize that AI systems should address the diverse needs of all people. Yet, efforts in this space often require sorting people into fixed buckets of pre-specified diversity-defining dimensions (e.g., demographics, personalities, communication styles), risking smoothing out or even stereotyping the rich spectrum of individualistic variations. To achieve an authentic representation of diversity that respects individuality, we propose individualistic alignment. While individualistic alignment can take various forms, in this paper, we introduce IndieValueCatalog, a dataset transformed from the influential World Values Survey (WVS), to study language models (LMs) on the specific challenge of individualistic value reasoning. Specifically, given a sample of an individual's value-expressing statements, models are tasked with predicting their value judgments in novel cases. With IndieValueCatalog, we reveal critical limitations in frontier LMs' abilities to reason about individualistic human values with accuracies, only ranging between 55% to 65%. Moreover, our results highlight that a precise description of individualistic values cannot be approximated only via demographic information. We also identify a partiality of LMs in reasoning about global individualistic values, as measured by our proposed Value Inequity Index ({\sigma}INEQUITY). Finally, we train a series of Individualistic Value Reasoners (IndieValueReasoner) using IndieValueCatalog to enhance models' individualistic value reasoning capability, revealing new patterns and dynamics into global human values. We outline future research challenges and opportunities for advancing individualistic alignment.