Why is the testing set standardized using fit values from the training set
You could do that. Assuming your train/test data are from the same distribution, which is in fact what you assume, they should have a similar mean and standard deviation. The result would be similar, in theory, so by the same token, why would you refit the scaling on test data?

In practice, the mean/variance estimate from the presumably smaller test set is probably not as accurate. You will be transforming the test data differently than the training data, and the model may not fit as well.

Taking it to a logical conclusion, how would you then predict for a single future instance? you can't scale one instance based on stats from one instance; it has no variance.

The principle here is to fit a model on training data and then apply that fixed model, of which scaling may be a part, to future data. So there is no particular upside to refitting this specially, and some potential downside.