Current chart-related tasks, such as chart generation (NL2Chart), chart schema parsing, chart data parsing, and chart question answering (ChartQA), are typically studied in isolation, preventing models from learning the shared semantics that link chart creation and interpretation. We introduce CycleChart, a consistency-based learning framework for bidirectional chart understanding and generation. Unlike conventional multi-task approaches that draw training samples independently across tasks, CycleChart organizes all tasks around each single data instance. From a source table and natural-language query, the model generates a chart specification, renders and executes it, then learns to recover the schema and underlying data from the resulting chart image. This per-instance lifecycle design lets the model capture the full chain of transformations, from raw data through visual encoding to structured recovery, and a generate--parse consistency objective enforces semantic alignment between the forward generation and reverse parsing directions. To support this framework, we construct CycleChart-Bench, a lifecycle-aligned benchmark where every chart sample carries aligned annotations for generation, schema parsing, data parsing, and question answering. CycleChart achieves strong results across all four tasks and transfers effectively to unseen external benchmarks, demonstrating improved cross-task generalization and marking a step toward more general chart understanding models.