Cosmology
Transmissions of power and authority at the communal level are usually symbolized by tithing and anointing. Tithing is a transmission of matter and power from below, in which portions of material resources are offered up to support the head. Anointing is a transmission of meaning and authority from above. Oil resembles golden light and makes what it covers glossy and reflective. Oil was also fuel for lamps, so like breath, it serves as a vehicle of light/meaning.
(The Language of Creation: Cosmic Symbolism in Genesis - A Commentary by Matthieu Pageau, 2018. Pages 85-87)
The story of anointing
The prophet Samuel anointed Saul (1 Samuel 10:1) and David (1 Samuel 16:13) to be king with a horn of oil. The Spirit of the LORD left Saul and was even replaced by a harmful spirit (1 Samuel 16:14), but he was still the LORD's anointed. (1 Samuel 24:6)