Medical image segmentation remains challenging due to the high cost of pixel-level annotations for training. In the context of weak supervision, clinician gaze data captures regions of diagnostic interest; however, its sparsity limits its use for segmentation. In contrast, vision-language models (VLMs) provide semantic context through textual descriptions but lack the explanation precision required. Recognizing that neither source alone suffices, we propose a teacher-student framework that integrates both gaze and language supervision, leveraging their complementary strengths. Our key insight is that gaze data indicates where clinicians focus during diagnosis, while VLMs explain why those regions are significant. To implement this, the teacher model first learns from gaze points enhanced by VLM-generated descriptions of lesion morphology, establishing a foundation for guiding the student model. The teacher then directs the student through three strategies: (1) Multi-scale feature alignment to fuse visual cues with textual semantics; (2) Confidence-weighted consistency constraints to focus on reliable predictions; (3) Adaptive masking to limit error propagation in uncertain areas. Experiments on the Kvasir-SEG, NCI-ISBI, and ISIC datasets show that our method achieves Dice scores of 80.78%, 80.53%, and 84.22%, respectively-improving 3-5% over gaze baselines without increasing the annotation burden. By preserving correlations among predictions, gaze data, and lesion descriptions, our framework also maintains clinical interpretability. This work illustrates how integrating human visual attention with AI-generated semantic context can effectively overcome the limitations of individual weak supervision signals, thereby advancing the development of deployable, annotation-efficient medical AI systems. Code is available at: https://github.com/jingkunchen/FGI.