“This is the law of the Torah that Hashem commanded saying: Speak to Bnai Yisrael. And they should take for you a perfectly red cow that has no blemish and has never had a yoke placed upon it.” (BeMidbar 19:2)
Parshat Chukat discusses the laws of the Parah Adumah – the Red Cow. This cow is burned. Its ashes are used in the process of purifying a person that has become defiled through contact with a dead body.
The cow that is burned and used in this purification process must meet specific requirements. Our pasuk describes these three basic requirements. The cow must be completely red. It must be unblemished. The cow must never have had a yoke placed upon it.
The need for the cow to be unblemished is not surprising. This is a requirement of animals used for sacrifice. It is reasonable for this requirement to be applied to the Parah Adumah. However, the restriction against using a cow that has born a yoke is unusual. This restriction does not generally apply to sacrifices. What is the reason for this restriction?
There is one instance of a similar restriction. This is in regard to the Eglah Arufah. This calf is slaughtered in the process of atonement for an unsolved murder. The Torah requires the calf has not been used for labor and has not drawn a load with a yoke.
These restrictions are similar. Both the Parah Adumah and the Eglah Arufah are disqualified through association with labor. However, the restrictions are not identical. A cow is disqualified from serving as Parah Adumah through placing a yoke upon it. It is not necessary for the cow to do any actual labor. In contrast, the mere placement of the yoke on a calf does not disqualify it from serving as an Eglah Arufah. The calf is only disqualified if it has actually drawn a load. This raises an additional question. Why is this unique restriction formulated differently in these two instances? Why does the mere placement of the yoke upon the Parah Adumah disqualify the animal? Why is the Eglah Arufah only disqualified through drawing a burden with the yoke?
Gershonides deals with our first question. Why is an animal associated with labor disqualified from use as a Parah Adumah and an Eglah Arufah? He explains the basic concept underlying this restriction. There is a fundamental distinction between animals used for sacrifice and the animals chosen for Parah Adumah and Eglah Arufah. An animal chosen for a sacrifice can have a previous identity or function. An animal that has been designated for work or used for labor can become a sacrifice. Only after the animal is chosen for sacrifice, does it receive a designation. After the animal is designated to be a sacrifice, it can no longer be used for labor. Using the animal for labor contradicts its designation as a sacrifice. In short, in the case of a sacrificial animal a previous identity does not disqualify the animal from receiving a new designation. It can still be designated as a sacrifice.
The cow chosen for the Parah Adumah cannot have been previously associated with labor. The use of the cow as a Parah Adumah must be the first and only identity of the cow. The placement of a yoke upon the cow confers an identity. With the placement of the yoke upon the cow, it is associated with labor. This is an identity in the animal. This disqualifies the animal. The identity of Parah Adumah or Eglah Arufah must be the first and only identity in the animal. Gershonides expresses the concept in an interesting manner. It must be as if the animal was created to serve as a Parah Adumah or Eglah Arufah. 
We will now turn to our second question. Why is the restriction of the Eglah Arufah formulated differently than the restriction upon the Parah Adumah? Why does the mere placement of the yoke upon a cow disqualify it from use as a Parah Adumah? Why is a calf disqualified from serving as an Eglah Arufah only after it has pulled a load?
Gershonides contends that the restrictions upon the Parah Adumah and the Eglah Arufah share the same underlying concept. The animal chosen for either of these functions must be free of a previous identity. He explains that the difference in the restrictions lies in the stringency with which this requirement is applied. In the case of the Eglah Arufah, the animal becomes associated with labor through the performance of labor. Therefore, only through the actual performance of labor is the calf disqualified. In contrast, the Parah Adumah is associated with labor through designation. Placement of the yoke upon the cow designates it for use in labor. This designation alone creates an association. The cow can no longer be used as a Parah Adumah.
In short, the two formulations differ in the degree of association to labor that disqualifies the animal. The restriction in regard to Eglah Arufah requires a higher degree of association. Only the actual performance of labor produces this degree of association. The restriction in regard to the Parah Adumah requires a lower degree of association. Even designation of the cow for labor creates this lower degree of association and disqualifies the cow.
“And Hashem came to Bilaam in the night. And He said to him, “If these men have come to call for you, arise and go with them. However, that which I will tell you, you should say”. (BeMidbar 22:20)
Balak sends messengers to Bilaam. He asks Bilaam to curse Bnai Yisrael. Bilaam responds that he must follow Hashem’s instructions. The Almighty appears to Bilaam. He tells Bilaam that he should not accompany the messengers. He cannot curse Bnai Yisrael. They are a blessed people.
Balak sends a second delegation. Again, Bilaam tells the messengers that he must wait for guidance from Hashem. Our pasuk contains the Almighty’s response. He tells Bilaam that he may accompany the messengers.
Bilaam leaves on his journey to join Balak. Immediately, the Torah reports that Hashem is angry with Bilaam for deciding to accompany the messengers. An angel of G-d appears to Bilaam. The angel threatens to kill him. Bilaam recognizes his mistake. He offers to abandon his mission and return home. The angel tells Bilaam to continue on his journey. However, he cautions Bilaam not to deviate from the message he will receive from Hashem.
This series of incidents presents a number of problems. First, the Almighty initially told Bilaam not to accompany the messengers. Then, Hashem apparently relented. He told Bilaam he can travel with the delegation back to Balak. How could the Almighty alter His decision?
Second, Bilaam embarked on his journey. The Torah tells us that Hashem was angry. Why was Hashem angry? He told Bilaam he could accompany the delegation! Bilaam had not disobeyed Hashem!
Third, an angel is sent to Bilaam. The angel persuades him that he had not acted properly. Bilaam understood the message. He confessed his sin. He offered to abandon his mission. We would expect the angel to accept this offer and to tell Bilaam to return home. Instead, the angel told Bilaam to continue on his journey! What was the objective in sending the angel? In the end the angel encouraged Bilaam to continue on his journey!
Nachmanides offers a brilliant but simple answer to these questions. He explains that the Almighty never intended to forbid Bilaam from joining Balak. Hashem actually wanted Bilaam to respond to Balak’s summons. Why? The Almighty wanted Bnai Yisrael to be blessed by this non-Jewish prophet. He wanted Balak to witness this event. This insight can be applied to answer all of our questions.
First, the Almighty initially forbade Bilaam from accompanying the messengers. The reason is found in Bilaam’s explanation of his mission. He told Hashem that he had been called upon to curse Bnai Yisrael. Hashem responded that this is a mission that Bilaam cannot fulfill. He should not accompany the delegation.
Second, Hashem never altered His position. The second time He spoke to Bilaam He told him that if the delegation has called upon him for assistance and counsel, he may accompany the messengers. He did not tell Bilaam he can curse Bnai Yisrael. Hashem specifically told him he can only repeat His words. This is consistent with Hashem’s objective. The Almighty wanted Bilaam to bless Bnai Yisrael in the presence of Balak. This required Bilaam to return with the delegation. However, it was made clear that he could curse Bnai Yisrael.
Third, Bilaam left on his journey. Hashem become angry. This was because Bilaam did not indicate to the delegation the conditions of his agreement to follow them. The delegates assumed that the Almighty had actually agreed to their request. This created a problem. Ultimately, Bilaam will not be permitted to curse Bnai Yisrael. The G-d of the Jews will appear quite capricious.
Third, the angel did not want Bilaam to return home. He demanded that Bilaam clearly state his limitations. Once the angel was convinced that Bilaam would tell Balak that he can not curse Bnai Yisrael, the angel allowed him to proceed.
We can now understand Bilaam’s first words when meeting Balak. He told Balak that although he had responded to his summons, he could not utter any pronouncement that is not authorized by the Almighty. Bilaam was fulfilling the commitment made to the angel.
 Sefer Devarim 21:3.  Rabbaynu Moshe ben Maimon (Rambam / Maimonides) Mishne Torah, Hilchot Parah Adumah 1:7.  Rabbaynu Moshe ben Maimon (Rambam / Maimonides) Mishne Torah, Hilchot Rotzeach U’Shmirat Nefesh 10:3.  Rabbaynu Levi ben Gershon (Ralbag / Gershonides), Commentary on Sefer BeMidbar, (Mosad HaRav Kook, 1998), pp. 94-95.  Rabbaynu Levi ben Gershon (Ralbag / Gershonides), Commentary on Sefer BeMidbar, (Mosad HaRav Kook, 1998), pp. 94-95.  Rabbaynu Moshe ben Nachman (Ramban / Nachmanides), Commentary on Sefer BeMidbar 22:20.  Rabbaynu Moshe ben Nachman (Ramban / Nachmanides), Commentary on Sefer BeMidbar 22:35.