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It's not a question of logic, it's a question of law. The Directors are the people appointed by the shareholders to conduct the business of the company. What titles the Directors choose to dish out to the managers that they appoint is up to them.
The CEO has no authority of any kind over the Directors in their capacity as Directors: Directors are answerable only to shareholders, not other directors.
As the most senior manager, the CEO (if the company has one) may have authority over other managers, who may also be Directors.
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