Extremely weakly-supervised text classification aims to classify texts without any labeled data, but only relying on class names as supervision. Existing works include prompt-based and seed-based methods. Prompt-based methods prompt language model with instructions, while seed-based methods generate pseudo-labels with word matching. Both of them have significant flaws, including zero-shot instability and context-dependent ambiguities. This paper introduces SetSync, which follows a new paradigm, i.e. wordset-based, which can avoid the above problems. In SetSync, a class is represented with wordsets, and pseudo-labels are generated with wordsets matching. To facilitate this, we propose to use information bottleneck to identify class-relevant wordsets. Moreover, we regard the classifier training as a hybrid learning of semi-supervised and noisy-labels, and propose a new training strategy, termed sync-denoising. Extensive experiments on 11 datasets show that SetSync outperforms all existing prompt and seed methods, exceeding SOTA by an impressive average of 8 points.