Hierarchical text classification (HTC) is a challenging subtask of multi-label classification due to its complex taxonomic structure. Nearly all recent HTC works focus on how the labels are structured but ignore the sub-structure of ground-truth labels according to each input text which contains fruitful label co-occurrence information. In this work, we introduce this local hierarchy with an adversarial framework. We propose a HiAdv framework that can fit in nearly all HTC models and optimize them with the local hierarchy as auxiliary information. We test on two typical HTC models and find that HiAdv is effective in all scenarios and is adept at dealing with complex taxonomic hierarchies. Further experiments demonstrate that the promotion of our framework indeed comes from the local hierarchy and the local hierarchy is beneficial for rare classes which have insufficient training data.