Why should the secondary of a voltage transformer not be short circuited?

A voltage transformer takes a primary voltage and steps it down to a smaller secondary voltage. This type of transformer will attempt to keep the secondary voltage at a specific ratio of the primary voltage. If you short it, massive current flow in the secondary is required to do this.

For a similar reason a CT should never be open circuited - because it attempts to push a specific ratio of primary current through the secondary. If you open circuit the secondary, it takes a massive voltage on the secondary to accomplish this.