When describing Achashveirosh's seudah, the pasuk states (Esther 1:8), לעשות כרצון איש ואיש, "to do according to the wish of man and man." Chazal (Megillah 12.) say איש ואיש, "man and man" refers to Mordechai and Haman. We can explain that Mordechai is called איש, which is roshei teivos for אושיום שין א, "There is no reason to despair." Haman is called ואיש, with a vav at the beginning. These letters spell יאו"ש. This demonstrates the difference between Mordechai and Haman. Mordechai signifies to us that there is always hope. As we wrote above, even if a person isn’t perfect, his good deeds that he does make him precious to Hashem. Haman wants man to feel there is no hope for him due to his aveiros.
Shortly after the Yidden left Mitzrayim, they were confronted with a war against Amalek, and Amalek attacked those at a low spiritual level. As it states (Devarim 25:18), ויזנב בך כל הנחשלים אחריך, "[Amalek] struck all...the weaklings in the rear." Rashi writes, "They were [spiritually] weak, and the clouds (ענני הכבוד) ejected them." Amalek gravitates to the spiritually low people to convince them that there is no hope for them. The Yismach Yisrael (Zachor 3) writes, "Amalek caused them to think that they lost their חלק אלו"ה, their G-dly soul..."
There is a mitzvah to erase the memory of Amalek and his descendants, but there is no mitzvah to obliterate Pharaoh’s memory. This is because Amalek is worse than Pharaoh. Pharaoh didn't believe in Hashem. He said (Shemos 5:2), מי ה' אשר אשמע בקולו', "Who is Hashem that I must listen to Him?" Amalek is worse because he causes people to lose belief in themselves.
Revid HaZahav (Haftarah Shabbos Shuvah) explains that the Megillah hints at the disheartening words Amalek (the yetzer hara) tells people to cause them to lose hope. Amalek says (Esther 3:3), למה אתה עובר את מצות המלך, "Why do you disobey the King's demand?" ויהי באמרם אליו יום יום, and he repeats these words every day. Mordechai replies, אשר הוא יהודי, you are a Yid. You perform mitzvos every day. It isn’t as bleak as Amalek wants you to think.
The Gemara (Megillah 12.) states, "The students asked Reb Shimon bar Yochai, 'Why were the Yidden of that generation deserving to die?'" The students knew that Haman's decree was also established in heaven. The Jewish nation of the time deserved annihilation, r"l, according to the heavenly court. The students wanted to know their aveirah, which made them guilty and deserving of such punishment. Reb Shimon replied, "You tell me!" They replied, "It is because they enjoyed the seudah of that rasha (Achashveirosh)." Reb Shimon said, "If so, the Jews in Shushan should die, and not the Yidden of the entire world." The students said, "So, tell us the reason." Reb Shimon said it is because they bowed down to Nevuchadnezzar's idol. The Alshich and several other sources say it was a combination of both aveiros – eating at Achashveirosh's meal and bowing down to Nevuchadnezzar’s idol.
The Chasam Sofer zt'l (Toras Moshe, beginning of Megillas Esther) says that the marvelous wonder of the miracle of Purim was that Hashem prepared the salvation at this party. Vashti was killed, opening a space for Esther, who saved the Jewish nation. So, at the place of sin, when Haman's decree was being established in heaven, the salvation of Bnei Yisrael was being arranged. This demonstrates Hashem's love to Bnei Yisrael, Who helps and saves them in every situation.
