The statement is true in some political contexts but not universally true in all jurisdictions.
The ability of a governor (or any executive authority) to remove someone from office whom they have appointed typically depends on the specific laws and regulations of the particular jurisdiction.
In many democratic systems, there are rules and legal procedures that govern the appointment and removal of public officials. These rules are designed to prevent arbitrary removals and maintain a system of checks and balances.
Therefore, while a governor or executive authority may have the power to make appointments, the process for removing appointees often involves certain criteria and procedures, such as misconduct, incompetence, or other valid reasons, which must be followed to ensure fair and just governance.