The rapid integration of generative artificial intelligence (AI) into creative workflows is transforming design from a human-driven activity into a synergistic process between humans and AI systems. Yet, most current tools still operate as linear “executors” of user commands, which fundamentally clashes with the non-linear, iterative, and ambiguous nature of human creativity. Addressing this gap, this article introduces a conceptual framework of five irreducible paradoxes—ambiguity vs. precision, control vs. serendipity, speed vs. reflection, individual vs. collective, and originality vs. remix—as core design tensions that shape human–AI co-creative systems. Rather than treating these tensions as problems to solve, we argue they should be understood as design drivers that can guide the creation of next-generation co-creative environments. Through a critical synthesis of existing literature, we show how current executor-based AI tools (e.g., Microsoft 365 Copilot, Midjourney) fail to support non-linear exploration, refinement, and human creative agency. This study contributes a novel theoretical lens for critically analyzing existing systems and a generative framework for designing human–AI collaboration environments that augment, rather than replace, human creative agency.