Recent advances in deep learning have greatly facilitated the automated segmentation of ultrasound images, which is essential for nodule morphological analysis. Nevertheless, most existing methods depend on extensive and precise annotations by domain experts, which are labor-intensive and time-consuming. In this study, we suggest using simple aspect ratio annotations directly from ultrasound clinical diagnoses for automated nodule segmentation. Especially, an asymmetric learning framework is developed by extending the aspect ratio annotations with two types of pseudo labels, i.e., conservative labels and radical labels, to train two asymmetric segmentation networks simultaneously. Subsequently, a conservative-radical-balance strategy (CRBS) strategy is proposed to complementally combine radical and conservative labels. An inconsistency-aware dynamically mixed pseudo-labels supervision (IDMPS) module is introduced to address the challenges of over-segmentation and under-segmentation caused by the two types of labels. To further leverage the spatial prior knowledge provided by clinical annotations, we also present a novel loss function namely the clinical anatomy prior loss. Extensive experiments on two clinically collected ultrasound datasets (thyroid and breast) demonstrate the superior performance of our proposed method, which can achieve comparable and even better performance than fully supervised methods using ground truth annotations.