HaShem's anger at Bilam stemmed from Bilam's active attempts to harm Israel, his advising the Midianites to entice the nation to sin.
SOURCES: R"A Friedman, as relayed by R"Y Medan
Chronology
This approach assumes that the interactions between Bilam and Balak in Bemidbar 22 take place at the same time as the story of the Sin of Baal Peor in Bemidbar 25, and that the stories must be interwoven to appreciate the full picture.
"ד בַר בִל עָם לִמ סׇר מַעַל בַי״י עַל ד בַר פ עוֹרהֵן הֵנָה הָיוּ לִב נֵי יִש רָאֵל בִ " – This approach, following Bavli Sanhedrin, understands this verse to mean that it was Bilam's idea to induce the Israelites to sin with the Midianites at Baal Peor. However, it uniquely suggests that this advice was given, not after Bilam's attempt to curse the nation failed, but at the very outset of the story. Already when HaShem initially forbade Bilam from going to curse the nation because "they are blessed" (22:12), Bilam suggested to Balak that he instead cause the nation to stumble and sin so that they would no longer be deserving of blessing.
"לֹא תָאֹר אֶת הָעָם כִי בָרוּךְ הוּא" – Though the text does not share that Bilam relayed this part of HaShem's words to the officers, this position assumes that he did. It is this knowledge that leads to the alternative plan of inciting to sin.
Did HaShem change His mind?
According to this reading, HaShem did change His mind between the first and second visits of Balak's messengers, but only due to a change in circumstances. During the first visit, Israel was free of sin and worthy of HaShem's protection, and so Bilam was prevented from cursing the nation. By the second visit, however, the nation had sinned at Baal Peor (in the wake of Bilam's advice) and were deserving of punishment. As such, HaShem acquiesced that Bilam be the tool to inflict it. HaShem, however, added a caveat: "וְאַךְ אֶת הַדָּבָּר אֲשֶר אֲדַבֵר אֵלֶיךָ אֹתוֹ תַעֲשֶה ", leaving room for the nation to repent and HaShem to change His mind again.
HaShem's wrath at Bilam
As this position uniquely suggests that Bilam not only had permission to go with the Moabites, but also to curse the nation, HaShem's ensuing wrath appears all the more misplaced. This position suggests that HaShem's about-face is once again the result of changed circumstances. By morning, when Bilam departed, Pinchas had killed the guilty parties at Baal Peor, appeasing HaShem's anger. As such, the nation was once again deserving of Divine protection. Moreover, HaShem's wrath at the nation was transferred to Bilam, who was guilty of causing them to sin to begin with.
Why doesn't HaShem have Bilam return home?
It is possible that after HaShem's anger at the Children of Israel was appeased and His love restored, He desired not only that the nation not be cursed, but that they be blessed instead. Thus, the angel tells Bilam to continue on his journey but to say only that which HaShem tells him, a blessing.
The encounter with the angel
This approach might suggest that the angel was sent to punish Bilam for his deed. However, we would have expected that at some point during the encounter, he would explain as much to Bilam. It is possible that the angel did in fact explain this, but this is omitted from the text, as it would not have been understandable given that the story of Baal Peor was recorded only afterwards in Chapter 25.
Why relay the message through a miraculous event?
It is unclear what purpose was served by miraculously opening the mouth of the donkey.
חָטָאתִי - a sincere confession?
This position might read Bilam's statement as an admission of defeat more than a confession.
Did Bilam change?
According to this position, though Bilam might have recognized that it was futile to curse Israel at this point, his presence on the side of the Midianites during the battle in Bemidbar 31 implies that his animosity towards Israel did not subside.
Moshe's recounting of the event
Moshe's words, "וְלֹא אָּבָּה ה' אֱלֹקיךָ לִשְמֹעַ אֶל בִלְעָּם וַיַהֲפֹךְ ה' אֱלֹקיךָ לְךָ אֶת הַקְלָּלָּה לִבְרָּכָּה ", are somewhat difficult for this approach as they imply that Bilam's plan failed and HaShem saved the nation from his machinations. Yet, according to this position, Bilam was successful in his plot to have the nation sin. As 24,000 people died as a result, it is hard to say that they were saved!
Bilam's death
The fact that Bilam is killed in the war against the Midianites, together with his partners in crime, is very fitting (Bemidbar 31:8).
Character of Bilam
This position does not merely read the later negative character of Bilam back into this story, but combines the two stories, presenting a wicked Bilam who not only seeks to harm Israel, but also actively causes Israel's downfall from the very beginning.
AGADAH: HOW OLD WAS BILAM WHEN HE DIED? (DAFYOMI.CO.IL)
QUESTION: The Gemara (Sanhendrin 106b) says that a Min asked Rebbi Chanina if he knew how old Bilam was when he died. Rebbi Chanina replied that although it is not explicitly stated anywhere, one may infer that Bilam was either 33 or 34 years old when he died. The verse states "Anshei Damim u'Mirmah Lo Yechetzu Yemeihem" -- "People of blood and crookedness, they will not have half of their days" (Tehilim 55:24). Since the average lifespan is 70 years, as the verse states, "Yemei Shenoseinu Shiv'im Shanah" -- "The number of our years is 70 years" (Tehilim 90:10), it stands to reason that Bilam lived less than half of those years. The Min informed Rebbi Chanina that he was correct; he personally had seen a written chronicle about Bilam which stated that Bilam was 33 years old when he was killed by Pinchas.
The Gemara here seems to contradict the statement of Rebbi Sima'i earlier (106a). Rebbi Sima'i states that three people were consulted about "that plot" (to enslave the Jews in Mitzrayim): Bilam, Iyov, and Yisro. Bilam advised that it was a good idea; later, as punishment for his advice, he was killed. Iyov, was silent, and was punished with suffering. Yisro ran away, and merited that his children would sit on the Sanhedrin in the Lishkas ha'Gazis. According to Rebbi Sima'i, Bilam would have been well over 200 years old when he died! Can these Gemaras be reconciled with each other?
ANSWERS:
(a) RASHI (DH Bar Tilsin) writes that it is clear that these Gemaras disagree. He says that according to Rebbi Sima'i, Bilam was over 210 years old, since Rebbi Sima'i maintains that Bilam was involved in the plot to throw the Jewish boys into the river.
The MELO HA'RO'IM has difficulty with Rashi's assertion that Bilam was over 210 years old. It was only a little over 80 years from the time of the decree to kill the Jewish boys until the Jewish people left Mitzrayim. This is clear from the fact that Moshe Rabeinu led the Jewish people out of Mitzrayim when he was 80 years old, and he was the last baby boy to whom the decree applied.
The DA'AS ZEKENIM (Shemos 1:10) and others seem to learn like the Melo ha'Ro'im. They agree, however, with Rashi that these two statements in the Gemara argue with each other, but they maintain that Bilam was about 140 years old when he died. The Da'as Zekenim explains that Bilam must have been at least 20 years old when he was asked for his advice. Another 80 years passed from the decree to throw the boys into the river, and another 40 years passed from the Exodus until the war with Midyan, which occurred at the end of the Jewish people's 40 years in the Midbar (see Bamidbar 31:2).
(b) The Da'as Zekenim quotes REBBI MENACHEM MI'DANI who says that these Gemaras do not disagree. When Rebbi Sima'i says that three people were consulted in the plot, he does not refer to the plot to enslave the Jews in Mitzrayim. Rather, he refers to the plot of "Lecha Iy'atzecha" -- "Let me advise you" (Balak 24:14), which hints to Bilam's advice to Balak that he could defeat the Jews by sending women to seduce them and have them serve Avodah Zarah, which would make Hash-m want to destroy them. Although Balak consulted Yisro and Iyov as well, they ran away or kept quiet. Bilam could have been very young at the time, and he could have died at 33.
However, this explanation conflicts with the Gemara in Zevachim (116b). The Gemara there states that all of the nations gathered to ask Bilam what was happening at the moment the Torah was given to the Jewish people. Bilam must have been at least 20 years old at the time, for otherwise they would not have sought his advice. This means that upon his death, he would have been at least 60 years old. Accordingly, it is difficult to reconcile these three Gemaras with each other.
(c) The ANAF YOSEF says that the Gemaras are not arguing. There were two individuals named Bilam. The second Bilam, who was killed by Pinchas, was a Gilgul (reincarnation) of the first Bilam who advised Pharaoh to throw the baby boys into the river. When the Gemara says that Bilam proclaimed "Keini (Yisro's descendants) -- you were with us in the consultation!" he meant that Yisro was with him in his former Gilgul. (Y. MONTROSE)
