Generative AI (GenAI) is transforming the creativity process. However, as presented in this paper, GenAI encounters "narrow creativity" barriers. We observe that both humans and GenAI focus on limited subsets of the design space. We investigate this phenomenon using the "Circles Exercise," a creativity test widely used to examine the creativity of humans. Quantitative analysis reveals that humans tend to generate familiar, high-frequency ideas, while GenAI produces a larger volume of incremental innovations at a low cost. However, similar to humans, it struggles to significantly expand creative boundaries. Moreover, advanced prompting strategies, such as Chain-of-Thought (CoT) prompting, mitigate narrow creativity issues but still fall short of substantially broadening the creative scope of humans and GenAI. These findings underscore both the challenges and opportunities for advancing GenAI-powered human creativity support tools.