There are contradictions in modern Tarology concerning the connection between Minor Arcana Suits and corresponding Elements.
And if everything is clear with the correspondence between the Suit of Pentacles and the element of Earth and the Suit of Cups and the element of Water, there is no common opinion with regard to the Suits of Swords and Wands.
In order to clarify this question, let us deal with the meaning of these two Elements:
Fire – energy, activity, impulse.
Air – chaos, movement, variability.
A sword is an instrument, which is used to convey an impulse of energy (in the form of a hit). There is also a clear connection between Fire and forged iron.
The Wands, however, have not always been the clubs portrayed by modern Tarot authors. In the Antique and Medieval Magical traditions, a Magical Wand was a willow twig which was used for locating underground water and finding treasure.
Such a willow twig was an agile, sensitive instrument, which started moving in the hands of a Magician when water or another object of search was located.
Movement and instability, in turn, are the main properties of the Element Air.
Thus, the correspondence between Swords and Fire, as well as between Wands and Air, is absolutely obvious for those initiated into the Magical Tradition.