The Maharal notes that Haman’s advisers must have known that Mordechai was a Jew, as Haman, himself mentioned to them (Esther 5:13). After all, it was possible that Mordechai was brought into Persia with King Yechanya (Esther 2:6), but was not actually a Jew. Therefore, the Talmud (Megillah 16a) understands the advisers’ remarks as relating to Mordechai’s tribal lineage. In effect, they were saying that if he were from the tribe of Yehudah, Binyamin, Efrayim, or Menasheh, Haman could not expect to be successful against him. In Bireishis (49:8), Yaakov promised Yehudah that his descendants would conquer their enemies. In Tehillim (80:3), King David prays that H-Shem strengthen Efrayim, Binyamin, and Menasheh. As it happens, Mordechai could trace his paternal lineage to one of these listed tribes and his maternal lineage to another.
The Maharal points out that Yehudah, Efrayim and Binyamin all represent Jewish unity because the Beis HaMikdash, and the Mishkan in Shilo and Nov were all located in their tribal inheritance. As proof, the Maharal quotes from the verse (Bamidbar 16:6) in which Moshe attempts to quell the rebellion of Korach and his group by saying they should all bring fire-pans. The entire group bringing individual fire-pans would represent the very opposite of unity. In fact, the unity of Jews’ uniqueness with H-Shem’s Uniqueness fights off the doubts and confusion that Amalek represents. The Midrash (Esther Rabbah 6:2) considers the description “Yehudi” as being derived from the adjective “yechidi” (“unique”) or the noun echad, (“one”).
According to the Targum, the advisers were not asking if Mordechai was a Jew, but if he were from the holier, saintly Jews. The Vilna Gaon writes that, unlike Haman’s assertion that the events he described were chance, Zeresh and the advisers were saying that it was not. After all, as a member of the Yehudim, Mordechai enjoyed the situation promised by the Talmud (Shabbos 156a, Nedarim 32a) that “ein mazal b’Yisroel” (“there is not mazal for Israel”).
R’ Dovid Feinstein explains that the advisers were focusing on the fact that Haman’s situation could go either way, based on Jews’ behavior.
The Ginzei HaMelech quotes R’ Meir Shapiro, who focused on the word, “zerah” (“seed”). They were saying that if the Jewish youth had no serious connection to Mordechai. They considered the aged Mordechai only powerful if he still held relevant sway on the youth of his people. So when Haman told them that Mordechai was surrounded by thousands of students learning a (temporarily) outmoded law regarding grains and Temple service, the advisers realized Haman has no chance. When Judaism is relevant for the invigorated youth, our enemies stand no chance.
Similarly, says the Ginzei HaMelech, Mordechai has to be mizerah (“from the seed”) of Yehudim – an invigorated member of the youth in vitality – and then Haman should just give up.
According to the Ben Ish Chai, Haman gave a short history lesson saying Mordechai was a descendant of Shaul, who only ruled briefly and not successfully. In response, the advisers said, that may be true, but Mordechai was also a descendant of Yehudah from his mother’s side, so he will win as promised. Homiletically, he reads the word im (if) as eim (mother).
According to the Alshich, there is an implied conversation between Haman and Achashverosh here. After Achashverosh tells Haman to honor Mordechai, Haman responds that Achashverosh should not desire to honor a Jew since Haman had acquired all of the Jews (see Esther 3:11), including Mordechai, to which Achashverosh responds that Mordechai is different since he “sits at the gate” – he is an adviser to the king, so he can be honored.
Answering this question, as well as the next, the Me’am Loez writes that Haman was implying that Mordechai was one to whom Achashverosh owes a debt – and no more.
The Talmud (Megillah 12b) states that Mordechai’s mother was from the tribe of Yehudah, while his father was from Benyamin. Although the tribal ancestry was paternal, members of the two tribes would later vie over his heritage to take credit for Mordechai’s greatness. The Alshich teaches that the verse is stressing that his mother was from the royal house of Yehudah. Rav Yehonasan Eibshutz says there is a mystical reason for this. According to the Talmud (Sanhedrin 99a), Haman’s female ancestor, Timna (see Bireishis 36:12 and Divrei HaYamim 1 1:36), also came from royal blood. Since, as Rav Elie Munk writes most cogently in Ascent to Harmony, “the division into masculine and feminine principles provides the pattern for all of creation” (80), the feminine aspect of Mordechai had to match the feminine aspect of Haman in order to defeat it. Therefore, Mordechai’s mother had to come from royalty to counter Haman.
R’ Yochanan’s opinion in the Talmud (Megillah 12b) is that Mordechai actually was from Benyamin, but was called a Yehudi because he fought against idol worship. According to Rav Yaakov Kaminetsky (in Emes L’Yaakov), the name “Yehuda” is especially apt for someone who stands against idolatry because the first three letters of the name (yud, hey, and vuv) are letters that spell the Name of H-Shem that represents His mastery over all, and is thus a rejection of pagan beliefs. The Chida adds that the gematria of Mordechai HaYehudi (40+200+4+20+10+5+10+5+6+4+10=314) is the same as Sha-d-ai (300+4+10=314), the name of H-Shem that connotes His ability to keep things from growing out of control, as in “He who said “dai!” (“enough!”)” while creating the borders of the world (Talmud, Chagigah 12a). Therefore, He controls everything, and can turn everything around, as He does through Mordechai and Esther in the Purim story.
The Sfas Emes gives three reasons for Mordechai’s being called “Yehudi,” all three relating the word in its guttural etymology to the word “echad,” (“one”). First, Mordechai was a “yachid,” (“a unique individual”) in that he saved an entire generation (see Midrash, Esther Rabbah 6:2). Second, he unified the Jewish people to counter Haman’s criticism that they were splintered in disunion (Esther 3:8). Finally, Mordechai sacrificed everything for H-Shem who is One, Echad (Devarim 6:4).