In this paper, we address Generalized Category Discovery, aiming to simultaneously uncover novel categories and accurately classify known ones. Traditional methods, which lean heavily on self-supervision and contrastive learning, often fall short when distinguishing between fine-grained categories. To address this, we introduce a novel concept called self-expertise', which enhances the model's ability to recognize subtle differences and uncover unknown categories. Our approach combines unsupervised and supervised self-expertise strategies to refine the model's discernment and generalization. Initially, hierarchical pseudo-labeling is used to providesoft supervision', improving the effectiveness of self-expertise. Our supervised technique differs from traditional methods by utilizing more abstract positive and negative samples, aiding in the formation of clusters that can generalize to novel categories. Meanwhile, our unsupervised strategy encourages the model to sharpen its category distinctions by considering within-category examples as `hard' negatives. Supported by theoretical insights, our empirical results showcase that our method outperforms existing state-of-the-art techniques in Generalized Category Discovery across several fine-grained datasets.