The Alshich writes that Esther said she will fast “similarly,” or more accurately, “with you” because of the oft-mentioned Talmudic concept (Baba Kama 92a) that when a person needs something, and decides to also pray for another who also needs that, this person’s prayer becomes more effective.
Ben Ish Chai again points out that the gematria of kein (“so”) (20+50=70) is seventy, the amount of hours Esther would fast.
The Beis Yaakov quotes a Talmud (source unclear) that bad breath becomes strongest after 72 hours, and this is why Esther does not fast for 72 hours straight.
The M’nos HaLevi writes that the reason Esther wanted the Jews to fast for her is, as it says in the Talmud (Baba Kama 92a), when we pray for someone else to have rachamim (“pity”), we earn rachamim, too.
R’ Dovid Chadida points out that Esther is really the only person in danger now. The Jews, after all, are only threatened in a year from this point. To answer why Esther wants the people to fast specifically for her, he quotes the Rambam’s commentary on the Mishna (Taanis 1:5) that a city can only establish a fast day for itself for one day. This only applies when it is a city in danger. However, when we pray for one person, the fast can last for multiple days.
The Me’am Loez brings another Mishnah (Taanis 2:1) that fasting alone is meaningless; the point is to pray, cry ,and perform teshuva (“repentance”).
Esther’s emphasis on fasting is to help the Jews realize that attending Achashverosh’s feast was the act for which they were to repent. Assuming she did not attend the feast, then, Ginzei HaMelech asks why Esther has to fast. He suggests the Jews went to the party because, on some level, they had a lack of faith in their relationship with H-Shem, thinking they were unworthy of His love and concern. According to the Ginzei HaMelech, Esther has been displaying a similar lack of faith in herself.
Incidentally, the Ben Ish Chai writes that she asked the Jews to fast eilai, for her, which can be spelled ayin (seventy) lee (“for me”), meaning that she, herself would only fast for seventy hours, which will be explained later, G-d Willing.
Rashi’s simple explanation is that Mordechai thinks Esther believes she will be safe in the palace on the day of the massacre. Rabbi Avigdor Bonchek, however, sees in Rashi’s words an irony that Esther’s safety can only be guaranteed through self-sacrifice.
The Vilna Gaon writes that Mordechai thought that Esther was under the impression that her volunteering herself to Achashverosh was one of the carnal sins for which one should sacrifice one’s life rather than sin, even for the sake of others.
The Sfas Emes points out that the Halacha (Shulchan Aruch, Yoreh Deah 157:1) requires a city under siege to refuse to give up any resident requested for execution by the attacking army. This is the case if this oppressive army does not specify their victim. However, if they they want a specific person, the community must give that person up to save themselves, since that person is threatened either way. This is only true when that person is threatened along with everyone else. Mordechai thinks Esther considers herself to be in this latter situation, safely tucked away in the palace.
R’ Dovid Feinstein writes that Mordechai was saying that H-Shem will save His people, as He always does. However, if Esther acts selfishly, she will not be among the other Jews.
Similarly, due to the fact that Mordechai mentions the king’s palace, and every mention of the word “king” is a reference to H-Shem, R’ Dovid Moshe Valle adds that the King can reach anywhere.
R’ Elisha Gallico notes that, in fact, Esther was actually in more danger staying in the palace. The reason for this, explains the Maharal, is that considering Achashverosh’s virulent hate for the Jews, Esther is safer away from the man who signed the edict to annihilate her nation. The Maharal compares this to living inside a basket with a snake. This is even moreso the case if Esther thinks of herself as an individual, and thus lacking the power of the united nation.
The Alshich says that, in Mordechai’s estimation, the root of Esther’s mission was to fix King Shaul’s error of allowing Agag to live.
According to Ginzei HaMelech, this is the reason why Mordechai is giving Esther such strong rebuke here; Esther needs to know that the only reason she was in that position was for this goal. Furthermore, Ginzei HaMelech points out that Torah is honest. Here, since Megillas Esther was written by Esther, herself, she nevertheless did not censor out this scene in which she looks weak. The Ginzei HaMelech furthermore adds that this case it was not appropriate to stay private.
R’ Menachem Ziemba was asked before the Warsaw ghetto uprising if the Chassidim should be involved in the fighting. He answered that it is indeed a mitzvah to give up one’s life when given the choice between death or their faith. When given no such choice, it is a mitzvah to fight.
According to the Kisei Shlomo, Mordechai was telling Esther she was responsible for Hasach’s death, and thus more invested now in the rescue of the Jews.
Rav Yitzchak Hutner writes in Pachad Ytizchak that when Person A needs something, and decides to also pray for Person B who also needs that, this makes Person A’s prayer more effective (Talmud, Baba Kama 92a). Rav Hutner explains that this principle works because prayer is stronger if it is performed with the whole heart (Talmud, Sotah 5b), meaning that it is more strongly felt. Therefore, Mordechai is telling Esther that she needs the same rescue as the Jews. In other words, she was already intent on praying for the Jews; what Mordechai wanted Esther to realize was that she was in the same precarious situation. Realizing that she also needs H-Shem to rescue her would cause Esther to feel that prayer with her whole heart, making her prayer stronger, and thus more effective.