Graph Neural Networks (GNNs) are becoming increasingly popular due to their superior performance in critical graph-related tasks. While quantization is widely used to accelerate GNN computation, quantized training faces unprecedented challenges. Current quantized GNN training systems often have longer training times than their full-precision counterparts for two reasons: (i) addressing the accuracy challenge leads to excessive overhead, and (ii) the optimization potential exposed by quantization is not adequately leveraged. This paper introduces Tango which re-thinks quantization challenges and opportunities for graph neural network training on GPUs with three contributions: Firstly, we introduce efficient rules to maintain accuracy during quantized GNN training. Secondly, we design and implement quantization-aware primitives and inter-primitive optimizations that can speed up GNN training. Finally, we integrate Tango with the popular Deep Graph Library (DGL) system and demonstrate its superior performance over state-of-the-art approaches on various GNN models and datasets.