In this paper, we propose a simple but powerful unsupervised learning method for speaker recognition, namely Contrastive Equilibrium Learning (CEL), which increases the uncertainty on nuisance factors latent in the embeddings by employing the uniformity loss. Also, to preserve speaker discriminability, a contrastive similarity loss function is used together. Experimental results showed that the proposed CEL significantly outperforms the state-of-the-art unsupervised speaker verification systems and the best performing model achieved 8.01% and 4.01% EER on VoxCeleb1 and VOiCES evaluation sets, respectively. On top of that, the performance of the supervised speaker embedding networks trained with initial parameters pre-trained via CEL showed better performance than those trained with randomly initialized parameters.