“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. 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.