The existing weakly supervised semantic segmentation (WSSS) methods pay much attention to generating accurate and complete class activation maps (CAMs) as pseudo-labels, while ignoring the importance of training the segmentation networks. In this work, we observe that there is an inconsistency between the quality of the pseudo-labels in CAMs and the performance of the final segmentation model, and the mislabeled pixels mainly lie on the boundary areas. Inspired by these findings, we argue that the focus of WSSS should be shifted to robust learning given the noisy pseudo-labels, and further propose a boundary-enhanced co-training (BECO) method for training the segmentation model. To be specific, we first propose to use a co-training paradigm with two interactive networks to improve the learning of uncertain pixels. Then we propose a boundary-enhanced strategy to boost the prediction of difficult boundary areas, which utilizes reliable predictions to construct artificial boundaries. Benefiting from the design of co-training and boundary enhancement, our method can achieve promising segmentation performance for different CAMs. Extensive experiments on PASCAL VOC 2012 and MS COCO 2014 validate the superiority of our BECO over other state-of-the-art methods.