Kybele and Kaaba are cognate words---that is, words that share the same root. But what is Kybele? Kybele is the correct Greek pronunciation for the name that is usually spelled Cybele and pronounced with an “s” sound. Kybebe is another form of the name. The root syllable means “cube”. It is easy to see why the Kaaba is called a cube. Perhaps the goddess Kybele had a cube-shaped temple on Mt. Ida in Phrygia (Turkey), where a black meteorite that was supposed to be her embodiment fell to the earth. The Kaaba was also built where a meteorite fell; it is lodged in the side of the structure, mounted in a curiously shaped piece of silver. The ancient writers knew that both stones existed and considered them to be a pair.
The Kabba was a temple to the goddess Al'lat before Muhammad converted or reconverted it to a shrine for the one God. The other 360 deities that were worshiped in Al'lat’s temple would have been “day gods”, each one representing one day. The five remaining days of the year would have been sacred to Al'lat and her consort Hubal. That, at any rate, was the way that the liturgical calendar of Kybele and her priest/consort Attis were arranged. It is my educated guess that if the two meteorites were nearly identical, as the ancient classical writers claimed, and both embodied a goddess, then the two goddesses would have been similar if not identical.
The Idaean stone was taken to Rome during the Punic Wars and ceremoniously housed in a temple to Cybele, whom the Romans called the Great Goddess and Mother of the Gods. In Latin her title was Magna Mater Deorum Idaea. Henceforth she would be the mother of Rome. Had history been different, Al'lat might have been the mother of Arabia. Muslims will assume that it was not God’s will that that should be so.
Below: the black stone in its sheath of silver.