Our Gemara on Amud Beis describes the ritual motions for shaking the four species:

⁦Rabbi Yoḥanan said: He moves them to and fro to dedicate them to He Whom the four directions are His. He raises and lowers them to He Whom the heavens and earth are His. In the West, Eretz Yisrael, they taught it as follows. Rabbi Ḥama bar Ukva said that Rabbi Yosei, son of Rabbi Ḥanina, said: He moves them to and fro in order to request a halt to harmful winds, storms and tempests that come from all directions; he raises and lowers them in order to halt harmful dews and rains that come from above.

Rabbenu Bechaye (VaYikra 23:40) discusses the kabbalistic meaning of this waving, and I will show, literally how it “ties” into our Gemara. The Esrog and the Lulav represents Adam the Tzaddik who sinned by קציצה בנטיעות “cutting down the saplings”, a Rabbinic euphemism for a certain kind of heresy, which we will define later. The date palm is the Tzaddik who stands tall, as in the verse (psalms 92:13), “ A Tzaddik like a date-palm”, and the Esrog is the fruit of the Tree of knowledge (Bereishis Rabbah 15:7). Because Adam sinned by “cutting down the saplings”, which caused a terrible disunity in God’s name, he must recreate the unity specifically by joining the four species together and waving them in all directions.  It also is significant that נקטם ראשו cutting the tip of the Lulav invalidates it (Shulkhan Arukh OH:645:6), unlike the myrtle branch (ibid, 646:10). This is because the three myrtle branches already represent unity, but the Lulav is the Tzaddik and cannot bear more cutting than what Adam already corrupted.

Now what is this euphemism, cutting the saplings, actually mean? Acher (the sage, Elisha ben Avuya)  is most famous for this violation as described in the incident of the four who entered the Pardes. His fate was to become a heretic, specifically in that he confused Mattatron as a deity (see Chaggigah 15a). Ramban Bereishis (11:2) attributes this similarly to the sin of the Tower of Babel, in trying to usurp God’s authority. Meshech Chokhma (Acharei Mos 4) explains in more detail. The sin of cutting the saplings, refers to attributing godly powers to naturalistic heavenly and physical forces. This fits in well with what Rabbenu Bechaye (Shemos 32:4) described as the sin of the golden calf and the ways Aharon became implicated.

Having understood this, we now can understand why the waving of the branches in all directions is described as a unification and a rectification of Adam’s sin of the cutting of the saplings. That is, showing that all the forces of Earth, wind and rain etc. all come from one source and one single unified God.

What remains unclear is how come the righteous in particular are so vulnerable to this sort of heresy? We find Adam making this mistake, and Acher, and Aharon almost sinning in this manner.  The best answer I can offer is that God is unknowable, completely removed and utterly mysterious. Any attempt to understand Him is rife with difficulty of minimizing His ability By attributing the actions in this world to secondary forces and messengers, or by lowering our understanding of God to make him comprehensible in this world. In this way, the common man who relies on the Biblical anthropomorphisms is sort of safe, because he’s following the Biblical stock descriptions, even if they can lead to problematic beliefs as Maimonides eloquently describes but Ravad defends in Hilchos Teshuva (3:7). However the sage must intellectually contend with all these paradoxical realities, and it could lead him to heresy. The effort and longing to know God as He is, can lead to confusion and many problems with the Biblical text. It is perhaps for this reason that the Tzaddik is more vulnerable to this problem of the cutting of the saplings.