In the Torah portion of Seitzei we read:1 “Do not wear a forbidden mixture, in which wool and linen are together [in a single garment].” This forbidden mixture is known as shatnez, or kilayim. The Torah goes on to state:2 “You shall make tzitzis on the four corners of the garment with which you cover yourself.” Because these verses are contiguous, we deduce that tzitzis may be made of kilayim.3

The Torah states that there are three forms of forbidden mixtures:4 “Do not plant kilayim in your vineyard.” “Do not plow with an ox and donkey together.” “Do not wear shatnez , where wool and linen are together.”

So too in the Torah portion of Kedoshim :5 “Do not breed your livestock in a manner of kilayim [ do not crossbreed]; do not plant your field with kilayim [do not hybridize plants]; do not wear a garment of kilayim [in which wool and linen are interwoven].”

Of these three forms, only “kilayim of garments” may at times be permissible, such as in the case of tzitzis. However, one may never produce hybrid animals or plants.

Why does “kilayim of garments” differ from the other two kinds?

The Ramban explains6 that the commandment prohibiting the crossbreeding of animals and plants is a logical one. G‑d created plants and animals so that they bring forth of “their own kind.”7 By producing a hybrid, one changes, denies and causes confusion in the Work of Creation. The prohibition of “plowing with an ox and donkey together,” is for the same reason; “a farmer generally places his draft animals in the same stable, and this can lead to interbreeding.”8

Thus, when one crossbreeds animals or plants he is causing chaos with regard to their reproduction — an essential element of their being. This flies in the face of the Work of Creation.9

This is not the case when one interlaces wool and linen. No essential intermingling is brought about; the two materials are merely superficially bound together. In fact, their connection is so tenuous that the threads can be severed one from the other.

Since the reason for the prohibition of “kilayim of garments” is not the same as that for the prohibition of crossbreeding plants and animals, for it merely serves to distance an individual from hybridizing,10 when it comes to a mitzvah such as tzitzis, the prohibition does not apply.

This will be better understood in light of the statement11 that the prohibition of kilayim involves not only physical intermingling, but also the improper mixture of two spiritual opposites. For wool and linen (and so too the ox and the donkey) allude to the diametrically opposite emotional attributes of kindness and severity. Since they are so different, they cannot be successfully combined.

This, however, must be understood,12 inasmuch as we find that combining two opposites results in one of the greatest qualities of all — the quality of peace. Thus we find that one of the main components of spiritual service is the combining of opposite attributes, to be neither too hard nor too soft.13 How then do we say that the prohibition of kilayim forbids the mixture of kindness and severity?

The impossibility of combining two opposite traits, however, only applies to the attributes as they exist in the world, but not as they are in holiness. For each worldly entity feels itself to exist separately unto itself. This feeling of self is so strong that it cannot combine with an opposite trait.

This is not so with regard to holy traits, for there the predominant aspect is self-abnegation and nullification of self to G‑dliness. In this instance, kindness and severity can commingle. Thus the Sifri states:14 “Only with regard to G‑dly attributes can love coexist with fear, and fear with love.”

Therefore, when kilayim is not for the purpose of a mitzvah, the opposite qualities inherent in each of the kinds makes it impossible for them to come together. They are therefore prohibited.

But when the opposites come together for the sake of a mitzvah, as in the case of tzitzis , then (as long as their union does not produce something contrary to G‑d’s will, as in crossbreeding), opposites can indeed make “peace” and come together in a permissible way.

Based on Likkutei Sichos , Vol. XXIX, pp. 122-127.