It is clear throughout Haman’s diatribe that he is attempting to malign the Jews for their lack of respect for the gentile king’s laws vis-a-vis their own laws. As Rav Hirsch (Collected Writings, Volume II, 423) writes, “by refusing to submit every aspect of its life to the laws of the king […] this nation, of course, demonstrates that there is indeed one area that cannot be touched by the laws of the state […and] if need be, will openly resist the king’s power […] This nation proclaims the truth that there is one power before which even a king’s majesty fades away.”
Although that is certainly one aspect of Haman’s claim, the very opposite can be simultaneously true, as well. In other words, as Rav Asher of Rofshutz explains, Haman was making the claim that the Jews were weak in their performance of the laws of – not the earthly king, but – the King in Heaven. In this, Haman is correct. After all, it was the Jews’ weakened observance that led to the threat on their very survival.
In Kol Sason, the author writes that the Jewish people always had two things protecting then – Torah and unity. Haman’s attack emphasizes that we had neither of these two. In a sense, all of the mitzvot of Purim – reading the Megillah, handing out gifts to the poor and our friends, etc. – are all about increasing Torah and unity.