Shalom and thank you for your question!
Yes, even if there is only 3 percent wool in your garment, it needs to be checked to rule out the presence of sha’atnez.
The source in the Torah for the mitzvah of sha’atnez in Deuteronomy, 22:11, where it states: “You shall not wear sha’atnez, wool and linen together.”
We find similar mitzvoth concerning the prohibition against harnessing two different kinds of animals together in order to plough, or sowing different kinds of seeds in the same place.
There are commentaries that give various insights, but before going into them I will point out that these mitzvot are in the category of chukim, as opposed to two other categories of mitzvot, called eduyot and mishpatim.
Chukim are mitzvoth which the human intellect would not have come up with on its own, and it is written that we perform them because “I have instituted a law and decreed a decree”, (says the L-rd.)
Edut are testimonials, mitzvoth that commemorate events in our spiritual history, that human intellect could theoretically have come up with, like keeping Shabbat, which commemorates G-d’s creating the world and resting on the seventh day.
Mishpatim are mitzvoth which human intellect would necessarily have come up with, such as not stealing or killing, respecting our parents, etc. The sages teach that were we not given the Torah, we would have learned modesty from cats and not to steal from ants.
Nevertheless, we are bidden to use our intellect to understand the Torah, for when we were privileged to receive it, we said “We shall do and we shall hear…” First – “We shall do…” because the Torah is G-d-given and it is G-d’s wisdom, so we first just accept it, but also “We shall hear…” that is, we shall learn it, delve into it, do our best to understand it and internalize it.
So what’s happening when we plough our field with an ox and a donkey? Each animal that was created has a different kind of energy. Some are among the ‘pure’ animals, that the Torah allows us to eat, and some are of the ‘impure’ kind, that we do not eat. The pure animals are usually animals that can be domesticated, and the impure sometimes are beasts of prey. Some commentaries feel that the prohibition against harnessing an ox with a donkey is because one is pure and one impure, but others disagree. However the common denominator is not to mix different kinds of energies, whether pure and impure, or the natures of the animals involved.
The Ibn Ezra points out also, that a donkey is weaker than an ox, and having to work together causes the donkey distress, while Rabbi Yosef Karo points out that an ox chews its cud, causing the donkey to feel that the ox is constantly eating while he is suffering!
In Deuteronomy 22:9, we learn not to sow our fields with different kinds of seeds together, and the commentary of the Chida sees this as an instruction to us, (relevant to Tu b’Shvat , where we learn that man is likened to the tree of the field,) not to mix Mitzvot with Aveirot, (sins,) such as giving to someone who needs it but slandering him as well. Learning Torah but taking pride in it is another example that he brings. He advises refraining from such actions, so that the good we do won’t become sullied.
When it comes to sha’atnez, the Torah actually instructs us to use it for certain purposes. In Deuteronomy 22:12 it states “Make strands for yourself,” referring to the mitzvah of tzitzit. The commentary of Rashi points out – “even from kilaim, mixed species. Chassidic teaching explains that linen is from a very high spiritual source which is not manifested in the physical world, when used for the mitzvah of tzitzit, it reveals that spiritual source, and therefore can be used together with wool, which is also from such a high spiritual source.
Wool and linen represent the G-dly energies of loving-kindness and severity, and thus should not be mixed in mundane matters where the creations see themselves as separate from G-dliness, but in matters of holiness, which involve nullification to G-d, these energies can be synthesized.
So, even though we have such fascinating insights, the law of sha’atnez is law, and in the instances where we are forbidden to use it, we must be careful even with 3 percent.
