“The lulav is a single palm branch and occupies the central position in the grouping. It comes with a holder-like contraption (made from its own leaves) which has two extensions. With the backbone (the solid spine) of the lulav facing you and this holder in place near the bottom, two willow branches are placed in the left extension and three myrtle branches are placed in the right.” 
The mitzvah in Torah  only mentions “4 species.”
Why do we specifically use 2 willow branches and 3 myrtle branches?
The answer is in the Zohar.
As a prelude to giving that answer, however, I think it’s necessary to insert a brief comment about Kabbalah and Jewish liturgy:
Kabbalistic literature is primarily about the 10 sefirot — the 10 Divine Emanations. While there are differences of interpretation, the model of 10 emanations is uniform. The most common one is “The Tree of Life,” which depicts them in descending order, with “Keter” at the top:
Rabbi Mosheh Cordovero famously illustrated them as occurring one-within-the-other, using the initial Hebrew letter of each one’s proper name in an increasingly “internal” sequence:
The entire creation — every possible universe and all of time — exists as no more than a microscopic speck (if even that much) in the lowest sefirah, “Malchut.”
Of the 10, the first or “upper” three — Keter (called “Ratzon” in early Kabbalah), Hochmah and Binah — are never “revealed” or “manifest.” We never “see” their activity directly, although we are its recipients (and often its initiators). The media through which we receive their “blessing” are the “lower” seven sefirot: Hesed, Gevurah, Tiferet, Hod, Netzach, Y’sod, Malchut. The upper three give what might be thought of as a blessing undifferentiated by circumstances, time or location; such differentiation occurs within the lower seven.
Thus, the numbers “7” and “10” have a very specific meaning in Kabbalah, with reference to the sefirot.
Many — perhaps most — Jewish observances predate the rise of Kabbalah as the form of Jewish “mysticism.” But with that rise, those observances were given another level of interpretation with regard to the sefirot, without, of course, denying or replacing earlier meanings. Where we see the number “7” present, we can be fairly certain that this was a Kabbalistic refinement of a practice that was already in place.
- The mitzvah of putting on tefillin already exists in rabbinic practice during the 2nd Temple period (I’m not sure that it existed in the same form during the 1st Temple period). But nowhere does it say to wrap the retzuah — the strap — around the left arm 7 times. That comes later, as a result of Kabbalistic teaching and practice.
- The Kabbalistic seder plate has six objects upon it, the seventh being the plate itself — plus the three matzot: 6+1+3+10.
- The “Kabbalat Shabbat” service, developed within the Safed community of Kabbalists in the 16th century (the most prominent member of which was the Ari — Rabbi Yitzhak Luria), consists mostly of six psalms representing the sefirot Hesed → Y’sod, followed by “L’cha Dodi” — representing “Malchut,” the “Divine Presence” or “Shabbat Queen.” Note that the “upper” three aren’t represented: They remain unmanifest in and of themselves, and are apparent only by their expression through the “lower” seven, of which “Malchut” is the culmination.
And so on.
Returning to the “lulav and etrog,” Torah  only mentions “4 species.” But if we take 3 myrtle branches + 2 willow branches + 1 etrog + 1 lulav, then 3+2+1+1 = 7.
It was most likely Kabbalists, then, who determined that there should be 3 myrtle and 2 willow branches.
As the Zohar says:
“There are four species in the lulav, which are seven [NAMELY, THREE BOUGHS OF MYRTLE, AND TWO BOUGHS OF WILLOW, LULAV AND ETROG].” 
My present post only makes the simple point above, without going into the far more intricate and interesting discussion of why the Kabbalists “read” the sefirot into observances and to what inspirational uses they intended us to apply this meaning.
But as a general statement, the Kabbalists wanted us to constantly remember that all of Creation is perpetually emanating from — and in — its Divine Source.
 Siegel, Richard, Strassfeld, Michael and Sharon, ed.’s; The Jewish Catalogue; © 1973 by The Jewish Publication Society; p. 73
(note: This is the “first” Jewish Catalogue; there was later a “second.”)
 Vayira/Lev. 23:40
 see: Zohar.com http://zohar.com/tzav-6
(note: the words in upper-case letters are interpolated into the translation of the text by the editors of Zohar.com, for purposes of explanation. Those words don’t exist in the text itself)