In the United States, primary open-angle glaucoma (POAG) is the leading cause of blindness, especially among African American and Hispanic individuals. Deep learning has been widely used to detect POAG using fundus images as its performance is comparable to or even surpasses diagnosis by clinicians. However, human bias in clinical diagnosis may be reflected and amplified in the widely-used deep learning models, thus impacting their performance. Biases may cause (1) underdiagnosis, increasing the risks of delayed or inadequate treatment, and (2) overdiagnosis, which may increase individuals' stress, fear, well-being, and unnecessary/costly treatment. In this study, we examined the underdiagnosis and overdiagnosis when applying deep learning in POAG detection based on the Ocular Hypertension Treatment Study (OHTS) from 22 centers across 16 states in the United States. Our results show that the widely-used deep learning model can underdiagnose or overdiagnose under-served populations. The most underdiagnosed group is female younger (< 60 yrs) group, and the most overdiagnosed group is Black older (≥ 60 yrs) group. Biased diagnosis through traditional deep learning methods may delay disease detection, treatment and create burdens among under-served populations, thereby, raising ethical concerns about using deep learning models in ophthalmology clinics.