Data Snooping, Information Leakage When Performing Feature Normalization
The normalization parameters you fitted in training are now part of your model. You fitted the model weights on the training data: the normalization step is part of your model now, and the "parameters" for that step are the mean and variance of the training data, not the test data. 

To help make this more concrete, let's pretend that this model is in production. You fit your model on whatever training data you had available, and now it's running as a scoring service. You can evaluate your model accuracy over time as data you've scored gets labeled to ground truth, but you're just evaluating the model not refitting it. How do you normalize these incoming predictions? You're going to need to use the mean and variance from whatever dataset you used to fit the model. If you'd rather do something like using the last K observations to estimate mean/variance, then that's the procedure you need to be testing when you fit the model.