Etymologically, the 'chair' was a real chair; the professor sat on it (the Sp catedrático reflects this); similarly, the bishop in a cathedral had such a chair*. It was a big and ornate chair - the Spanish cadera took a different path (one that involved more phonological erosion [I'm tempted to make a joke about hip-replacement, {cadera=hip} but I might be one of the few people to smile rather than look askance ]).

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PS * I believe the Pope sits in this sort of chair to make pronouncements ex cathedra [='from the chair']. That's Latin, but it's understood and used by the more lettered among us.