Nombres 19:2

This is the statute of the Torah. Because Satan and the nations of the world taunt Israel, saying, “What is this commandment? What is the reason for it”? Therefore, the Torah referred to it as חֻקָּה, a statute. I have decreed it, and you are not permitted to question it.

They shall take to you. It will always be called by your name: ”The cow which Moshe prepared in the wilderness.”

Red, perfect. It must be perfectly red. If it had two black hairs, it was disqualified.

This is the decree, the publication of the law which the Lord hath commanded, saying; Speak to the sons of Israel, that they bring to thee from the separation of the fold a red heifer, two years old, in which there is neither spot nor white hair, on which no male hath come, nor the burden of any work been imposed, neither hurt by the thong, nor grieved by the goad or prick, nor collar (band) or any like yoke.

This is ‘chukath’ (the statute of) the law. “Since Satan and the nations of the world ridicule Israel, saying, ‘What is [the meaning of] this commandment [of the Red Heifer]?’ therefore the Torah uses the term chukah (statute) in connection with it, [meaning]: ‘It is a decree from before Me, and you have no permission to question it.’” This is Rashi’s language, taken from the words of our Rabbis. 7; Yoma 67b. See also Vol. II, p. 208, Note 236. Now I have already written in connection with the goat that is sent away [to Azazel the reason] why the nations of the world should taunt us about this [commandment] more than [they taunt us about] the rest of the offerings which effect atonement, and some of which bring about purification — such as the offerings of a man [or woman] who suffered a flux,, 15:13-15; 25-31. or of a woman after childbirth., 12:6-8. [The reason is] that since [the procedure of the Red Heifer] is performed outside [the Sanctuary], it appears to the nations that it is slaughtered to the satyrs which are in the open field., 17:5-7. But the truth is that [the Red Heifer] is brought to remove the spirit of impurity, and the burning thereof outside [the Sanctuary Court] is like the sweet savor, 1:9 etc. — In other words, as long as the observance is in accordance with the word of G-d, it does not matter if it is done within the Sanctuary Court or outside thereof, for both were equally commanded by Him. [of the offerings brought within the Sanctuary Court].
The reason for the impurity conveyed by a corpse is [due to man’s sin committed through] the instigation of the serpent, for those who die by “the Divine Kiss” do not [in fact] convey impurity according to the law, this being the [sense of the] saying of the Rabbis: “The righteous do not convey impurity [when dead].” It is for this reason that Scripture states, This is ‘chukath’ of the law, meaning: [this is] that which is “hollowed out” — “to engrave, hollow out.” from the [Written] Torah, namely, the Oral Torah. Therefore it is a [female] heifer and must be red, [symbolic] of the attribute of justice. It is given to Eleazar inasmuch as it must be slaughtered before him, even [though it may actually be slaughtered] by a non-priest, because the deputy High Priest [i.e., Eleazar] supervises the performance thereof, so that it should be done in accordance with his intentions, and so that they should not entertain any …

זאת חקת התורה, in verse 14 the Torah already explains the purpose of the red heifer, i.e. which statute of the Torah is being introduced here.

פרה אדומה; this animal is required so that its ashes can be used to purify people who had become ritually defiled through direct or indirect contact with the body of a deceased human being.

'זאת חקת התורה אשר צוה ה, when the Torah in Nuimbers 8,7 had spoken of the need to sprinkle the waters of “chatat” on the Levites in order to purify them before they would begin their function newly assigned to them, our sages (Yuma 16) had already referred to the procedure as a chukkah, a statute, adding that these kinds of statute must not be questioned and probed as they are in the nature of a decree issued by G’d. The wise King Solomon, when mentioning that he had striven to unravel the wisdom in this legislation admitted that he had failed, that it was beyond him. (Kohelet 7,23). The thing which is most baffling in the red heifer legislation is that most who is ritually pure becomes ritually contaminated by direct contact with it, although the whole purpose of the red heifer, its ash, etc., is to purify the people who had been ritually contaminated prior to being sprinkled with spring water containing its ashes.
However, when we examine the entire commandment in detail we find that some of the people concerned with that red heifer from the moment it has been burned after having been slaughtered become ritually contaminated, i.e. the person burning its carcass, the person collecting its ashes, as well as the ones throwing the cedar wood as well as the one using the hyssop and crimson thread. into its burnt ashes. The same applies to all those either touching the remains or carrying them.
By contrast, the person performing the sprinkling with the mixture of the ash and water as well as the one sanctifying the location where the red heifer is to be burned and the one lighting the fire prior to burning the slaughtered red heifer are not contaminated by their activities.
One of the principal conditions concerning the red heifer is the requirement that it must not even have 2 hairs that are white or black. The symbolism of the colour red is supplied by the prophet Isaiah 1,18 who writes that even if your sins are as red as certain type or wool dyed red they can become white as snow under certain conditions of remorse.
Our sages considered this line so important that they used to tie a red string to the entrance of the Sanctuary when the scapegoat was thrown down on the Day of Atonement. This string would turn white as proof that the people’s sins had been forgiven. When this happened the people would rejoice for the remainder of that day, whereas when it failed to turn white they would be greatly saddened. (Yuma 67)
We must remember …