Mordechai tells Esther not to reveal her origin (Esther 2:10) ostensibly in the hopes that they would assume she was of ignoble birth and dismiss her (Rashi ad loc.). Once she is chosen by the king, why doesn't she (perhaps with Mordechai's permission) tell the king she is Jewish at that point? Wouldn't that have placed the Jews in a positive light in the kingdom and perhaps avoided Haman's plot in the first place?
In sum, why didn't Esther reveal her origin earlier?
The following is culled from Oz V'hadar's Mesivta on Megillas Esther, page 37, note 89; pages 230-232; and pages 251-252. Unless otherwise specified, the mefarshim are on Esther 2:10.
Mordechai wanted people to think that she was from a lowly family, and not from Sha'ul HaMelech. Had Achashveirosh known she was Jewish, that may have impacted her odds of becoming queen (Rashi, Rid). According to Rashi, presumably, Mordechai wanted to know if Esther's coronation was min hashamayim (see #7 below). The Rid says clearly Mordechai didn't want Esther to be queen and knew that revealing this information would mean her odds would go up for being picked.
Were Achashveirosh to kill her like he did Vashti, he may have gone after her entire nation (Targum Rishon and Sheini).
Mordechai did not want a position of authority. Were Achashveirosh told that Mordechai raised her, he would have been granted a position in his court (Yalkut Remez 1023, Manos HaLevi).
It would be easier for her to practice her religion if Achashveirosh didn't know what it was (R' Sa'adiah Gaon, Ibn Ezra, Rabbeinu Bachaye, Maharam Cheliav).
Mordechai was afraid that Achashveirosh, in his love for Esther, would decree that all of his officers should marry into her people (Rokeiach).
If a bad decree were placed on the Jews, Esther would A) not be placed under the decree, and B) have the upper hand in getting the decree revoked, as they would rescind it upon hearing that she was Jewish herself (Rokeiach).
Were Achashveirosh to know that she was Jewish, he wouldn't marry her, but nevertheless he would have relations with her. She would thus be humiliated (Tosfos HaShalem 2:10:3, Lekach Tov, Rishon LeTzion). And even if he wanted to marry her, his anti-Semitic advisors might give him some pushback (Chachamim of France, Ri Nachmiash to v. 8, Menachem ben Chelbo, R' Yosef Kra). It was important to Mordechai that she be queen so that she could be the conduit for good things between Achashveirosh and the Jews (Ralbag, R' Elisha Glikow). But if they knew that she was Jewish, she would have the opposite effect - they would hate the Jews even more (R' Sa'adiah Gaon).
Mordechai wanted the option of kidnaping her and escaping to another kingdom if need be. If Achashveirosh knew she were Jewish, he would kill the Jews were she not returned (R' Avigdor Kohen Tzedek). That's why Mordechai was always hanging about the palace gates (Tosfos HaShalem 2:19:7).
If Achashveirosh were to decree an evil decree on the Jews, he would single out Shevet Binyamin to be exempt. Were Esther to plead for her people, Achashveirosh wouldn't listen, as he would say that he already exempted her Shevet (Alshich to v. 11, R' Sa'adiah Gaon).
Other nations, afraid of Esther's potential to knock down their standing before the king and to turn him against them, might spread rumors against her until she is killed like Vashti was (Maharal).
They needed to take Esther against her will; she did not come willingly. Were she to reveal her nation, Achashveirosh might take revenge against them that they held back his future queen (Gra, Yosef Lekach).
Everyone loved Esther and thought she was a part of their people. The ruse would only work as long as she didn't reveal her nation (Maharsha to Megillah 13a "Esther").
Mordechai reasoned that in light of all of the anti-Semitism, and that they didn't know what was to be in store for them, having someone in the palace secretly being a Jew would be an advantage over their enemies (pseudo-Rambam).
If their enemies didn't know that Esther was Jewish, they would have no problem discussing their evil plans in front of her (Rishon LeTzion).
Haman had given Achashveirosh the advice to kill Vashti and replace her with another queen. If Achashveirosh didn't know his wife's nationality, she could have been from Haman's people, for all he knew, and thus Haman's tool to overthrow him (Mahari Asad).
Mordechai had no idea why Esther shouldn't reveal her nationality; he had received a nevuah to that effect, but was unclear on why it was necessary. To the contrary - it would have been better for her to say she were Jewish and the anti-Semitic king to refuse to marry her (Megillas Sesarim).
Mordechai wanted to keep tabs on Esther. Were their marriage revealed, Achashveirosh would have prevented him from entering the palace. Now, Esther had been taken from Mordechai's house; is it not obvious that there's some connection between them? But they didn't bring any of the women to Achashveirosh; they brought them to Hagai, who could not be expected to remember where all the women came from.
As long as it was doubtful if she would become Achashveirosh's queen, she was still mutar to Mordechai. If she were to reveal her nation and that she descended from royalty, she would definitely be his queen and would be assur (Ksav Sofer, based on Tosfos to Kesubos 51a "Assurah").
If Achashveirosh had relations with Esther for his own pleasure, Esther would be considered an Anusah, as she was taken against her will. Once she revealed her nationality, she risked him having relations to draw her away from her religion, which would require her to give up her life rather than concede. Mordechai saw through Ruach HaKodesh that she was important for Hashem's plan, and therefore she needed to be alive rather than die al kidush Hashem (Yedei Moshe).
TL;DR: You just asked a LOADED question that just about everyone talks about.
According to the Targum Sheni (2:10) Mordechai was concerned with Esther revealing this because the king would become upset with Esther at some point and direct his anger out on her people. Just as (later) Haman directed his hatred against Mordechai to the rest of the Jewish people, the king could do the same with Esther.
I always wondered if Mordechai told her to keep her family a secret because he wanted Esther to become queen and thought if it was found out that she was Jewish it would ruin her chances.
This article presents an interesting, thought-provoking angle.
Essentially, he claims that the Megillah mentions that after Ahashverush made Esther queen, it states that he sent gifts. The next verse says that Esther still didn't reveal her nationality as Mordechai had commanded her. What is the connection of these two verses?
The idea is that by giving gifts, Ahashverush hoped to embrace the Jews to reveal Esther's identity. After all, they all knew who Esther was! Yet, Mordechai not only told Esther not to reveal anything, but he told the Jews not to reveal anything, either.
At the end, this added to Ahashverush's anger towards Haman, because he was surprised that his own Queen was Jewish and that she was one of the people who Haman wanted to kill.
