The Talmud derives the rule that two hairs disqualify (but one does not) by analogy to other areas of Jewish law where the Torah uses a minimum threshold of two, establishing that 'two' is the legally meaningful unit of plurality.
וְאָמַר רַב הוּנָא: מַאי טַעְמָא דְּבֵית שַׁמַּאי? ״קַרְנֹת״, ״קַרְנֹת״, ״קַרְנֹת״ – הֲרֵי כָּאן שֵׁשׁ: אַרְבַּע לְמִצְוָה, וּשְׁתַּיִם לְעַכֵּב. וּבֵית הִלֵּל אוֹמְרִים: קַרְנוֹת, קַרְנַת, קַרְנַת – הֲרֵי כָּאן אַרְבַּע. שָׁלֹשׁ לְמִצְוָה, וְאַחַת לְעַכֵּב.
And Rav Huna says: What is the reasoning for the opinion of Beit Shammai? The verse states: “And the priest shall take of the blood of the sin-offering with his finger, and put it on the horns of the altar” (Leviticus 4:25); and “The priest shall take of the blood thereof with his finger, and put it on the horns of the altar” (Leviticus 4:30); and again: “The priest shall take of the blood of the sin-offering with his finger, and put it on the horns of the altar” (Leviticus 4:34). As the minimum amount justifying the use of plural, i.e., “horns,” is two, one may conclude that there are six references to the horns of the altar here. Four of them are mentioned for the mitzva, meaning that he should present the blood on all four horns of the altar ab initio, and the other two were mentioned to invalidate the offering if he did not present it on at least two horns. And Beit Hillel say: The matter should be understood according to the written consonantal text. The word “horns” is written once plene, with a vav, which means that it must be read in the plural; and the other two times the words “horns” and “horns” are written deficient, without a vav, in a way that can be vocalized in the singular. Therefore, there are four references to horns here. Three of these presentations are written to indicate that they are performed only as a mitzva, i.e., they are performed ab initio, but the offering is valid even absent their presentation. And the remaining one, i.e., the fourth presentation, is written to indicate that its absence invalidates the offering, i.e., the offering is not valid if the blood was not presented against at least one horn of the altar. Evidently, Beit Shammai hold the vocalization is authoritative, whereas Beit Hillel hold the consonantal text is authoritative.