The message "This Pokémon cannot be traded" is an error trap and is displayed for when the player attempts to upload a Pokémon with invalid data onto the Global Trading System, or more commonly when the player attempts to upload a hacked or 'abnormal' Pokémon onto the system.
Its purpose has not been fully explained by Nintendo, however it presumably exists to stop players from illegitimate Pokémon onto the Global Trading System. However, not all hacked Pokémon are blocked by this error trap. A similar message will appear when the player attempts to upload a Pokémon with a Classic Ribbon or a Premier Ribbon on to the Global Trading System as "It has a special Ribbon. It can’t be offered for a trade."