According to Megillas Sefer, Haman was saying to Esther that if she forgives him, Achashverosh will, too.
The Vilna Gaon writes that Haman tried to tell Esther that he didn’t know that the Jews were her people.
The Meshech Chochmo writes that Haman realized that the invitations came from Esther, so she is the one with the most power.
According to the Ben Ish Chai, Haman tried to convince Esther that he put her in this position of power by getting rid of Vashti, so she owed him a favor. The Malbim posits that perhaps Haman would not have approached her under any normal conditions, but she was the only one left, so he tried his alternative (Plan B) excuses on her. Seeing that she is a woman, and particularly a Jewish woman, he was hoping she would show Haman mercy.
The Sfas Emes writes that Esther fought the urge to be merciful, unlike Shaul with Agag. She accomplished this by having been exposed to Haman. In this way, she emotionally hated what she was intellectually commanded to hate. Similarly, first the verse (Devarim 25:17) commands us to remember Amalek, and only then (Devarim 25:19) to destroy it. First, one is required to have the emotion, and then to perform the act.
The Sfas Emes points out that, on a spiritual level, this act of Esther’s was a tikkun (“repair”) for Shaul’s error of allowing Agag to live. The Zer Zahav adds that Haman’s begging was a great test for Esther’s sense of improperly placed mercy. After all, the Rambam (Mishneh Torah, Hilchos Teshuva 2:1) writes that the ideal way to demonstrate complete repentance is to be faced with the same challenge, and to nevertheless overcome it, and this was almost a direct parallel to the story of Shaul and Agag.
Many cultures in large nations like Achashverosh’s would have their own unique set of rules, customs, and even mores. Here, Haman is stressing that Jewish laws not only different, but even antagonistic to the laws of the land. According to the Talmud (Megillah 13b), Haman is complaining that the Jews “won’t eat our food, won’t marry from us, won’t marry to us.” Haman even uses his knowledge of Jewish law to defame Judaism. He tells the king that if a fly were to touch a Jew’s cup, he would remove it and continue drinking. However, if the king were to touch a Jew’s cup, the Jew would throw the wine away. Alluding to the law of yayin nesech (see Talmud, Avodah Zarah 30a), Haman is telling the king that the Jews view the Persians as unclean (see the Targum Sheini).
According to Rav Dovid Feinstein, Haman is saying the Jews view their own laws as superior, and therefore even trumping, the king’s gentile law. On one hand, he is right. Although the Talmud in numerous places (Gittin 10b, Baba Kama 113a, Baba Basra 54b, Nedarim 28a) notes a concept called “dina d’malchusa dina” (“the law of the kingdom is the law”) which means is that Jews are expected to follow the laws of the lands in which we find ourselves, this is only true as long as those laws do not directly contradict Jewish law.
On the other hand, as Megillas Sefer learns, Haman is saying that the Jews even go to the extreme measure of mutilating their sons (through circumcision) to avoid intermarrying with the gentiles around us. Poor, little innocent children are cut for their parents’ religious fanaticism. Interestingly, had it not been a command, its cruelty would make it abhorrent. Rav Hirsch (Collected Writings, Volume II, 385) writes, “In exile, in disrepute, tiny to behold, yet always conspicuous, it is a nation which calls attention to itself, prods others into action and yet, despite its dispersal, manages to preserve its unique heritage and even to transmit it from one generation to the other.”
The Targum Sheini writes that Haman’s criticism of the Jews here was that the Jews “have warm water in winter and cold water in summer.” The Ben Ish Chai explains that Haman is saying the Jews focus on physical pleasure. He also says notes that the Jews manipulate their own calendars from twenty-nine to thirty days, depending on when they want Rosh Chodesh to fall out. In Haman’s estimation, these designations are arbitrary and to the Jews’ own benefit.
The Vilna Gaon points out that, had Haman seen Mordechai not bowing to him, the servants would have no need to report this information to him. However, filled with self -love and pride, with his chin in the air, Haman never even bothered to see this phenomenon for himself!
Megillas Sefer says that the king’s servants were acting out of a sense of curiosity. In the Book of Daniel (3:19-23), Chananya, Mishael, and Azarya all survived the fiery furnace of Nebuchadnetzer. These servants wanted to see if the same would hold true for Mordechai, as well.
Me’am Loez notes that it is interesting that they reported Mordechai’s conduct to Haman rather than to the king who issued the decree Mordechai is ignoring. Had they told the king, Mordechai would have been summarily executed. Informing Haman allowed the possibility that Mordechai would have been tortured until he submitted. Psychologically, these servants could then feel better about themselves and their behavior. This, coupled with preserving the status quo, is a powerful motivator. From their selfish perspective, it would certainly be better than turning Mordechai into a martyr.