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We learned earlier that the forbidden mixture of wool and linen, or shaatnez, is allowed in tzitzit, because the two commandments follow each other in the Torah, forming a "this is prohibited, [but] this is allowed" pattern. However, this is only the opinion of Beit Hillel. Beit Shammai, who do not derive conclusions from the proximity of phrases, consequently, do not allow Shaatnez in the tzitzit.
But practically, anybody who would put a blue woolen thread in his linen tzitzit, aroused astonishment in Jerusalem of old. Jerusalem was the place of especially pious people, and they did not use the Beit Hillel's permission. Why not? Must be that in practice Beit Hillel also forbade this.
The sugya in our daf presents what appears, at first glance, to be a deceptively technical debate. A baraita records a dispute between Beit Shammai and Beit Hillel concerning whether a linen garment (sadin) is obligated in the mitzvah of tzitzit. The crux of the disagreement is straightforward: the tekhelet (sky-blue) thread required for tzitzit must be made of wool, and attaching wool threads to a linen garment would produce shaatnez—a prohibited mixture of wool and linen (Deut. 22:11). Beit Shammai, sensitive to this prohibition, exempt the linen garment from tzitzit entirely. Beit Hillel, by contrast, obligate it, invoking the principle that the positive commandment of tzitzit overrides the prohibition of shaatnez. The halakha is declared in accordance with Beit Hillel.