The collection and curation of high-quality training data is crucial for developing text classification models with superior performance, but it is often associated with significant costs and time investment. Researchers have recently explored using large language models (LLMs) to generate synthetic datasets as an alternative approach. However, the effectiveness of the LLM-generated synthetic data in supporting model training is inconsistent across different classification tasks. To better understand factors that moderate the effectiveness of the LLM-generated synthetic data, in this study, we look into how the performance of models trained on these synthetic data may vary with the subjectivity of classification. Our results indicate that subjectivity, at both the task level and instance level, is negatively associated with the performance of the model trained on synthetic data. We conclude by discussing the implications of our work on the potential and limitations of leveraging LLM for synthetic data generation.