R’ Tzadok haKohein (Resisei Layla #52) explains that there is a gate of Torah that corresponds to each nation of the world, and through the power of each gate’s Torah the goodness of that nation is redeemed and becomes part of the Jewish nation. The 50th gate of wisdom, which was not revealed even to Moshe, is the gate which corresponds to Amalek. There has not yet been revealed in the world the chochmas haTorah that can redeem Amalek, and hence they must be destroyed. Moshe Rabeinu, who embodies the chochmas haTorah, could not lead the battle against Amalek because he lacked this 50th level, and therefore appointed Yehoshua to do so. Yehoshua was the meshameish of Moshe, the attendant who clung to his master and exhibited the selfless dedication of a pure desire to learn. Gadol shimusha yoseir m’limuda, R' Tzadok explains, means that the desire to learn is more powerful than the act of study itself, and through that power, Amalek can be destroyed.
I think what R’ Tzadok is telling us is that Amalek preaches to our own shortcomings. Amalek feeds our sense of despondency and yeiush with the knowledge that as Torah and Hashem are one, as surely as we are human and can never attain that 50th gate of Torah, we can never truly have a relationship with Hashem. On the pasuk “Vayelech Agag ma’adanot” the Ishbitza writes that Agag professed a “givun tov”, an outer daintiness that concealed his inner evil. Amalek tells us that we are all just pretenders wearing a “givun tov”, a mask of goodness, for even people we consider models of righteousness still fall short in G-d’s eyes. If so, why bother to try?
Gadol shimusha yoseir m’limuda means that closeness to G-d does not come only from achievements and ability, but comes from desire as well. And where ability and achievement fall short, desire can more than make up the difference. The battle against Amalek, writes R’ Tzadok, was always carried on by descendents of Rachel – by Shaul, by Mordechai, by Esther, who embodied the tzniyus of Rachel. Leah gave birth to the majority of shevatim in Klal Yisrael, but Rachel had within her the burning desire to be able to fill that role.
On Purim we don masks because, as the Ishbitza writes, a Jew is the opposite of Amalek. Whereas Amalek proclaims that goodness is just a mask over man’s inherent shortcomings, a Jew says that shortcoming is just a mask over the inherent goodness of each of soul.