Tosfos quotes the mishna in Kelayim which says that garment sellers can wear shatnez as long as they don't have kavana to get hana'a from the protection from the rain or sun. So if kelayim is only assur when you get hana'a from the garment, why is there ever a problem of kelayim by a talis if you only wear it in order to do the mitzva of tzitzis, and a mitzva is not considered hana'a?
Tzvi Hertzberg, New York, USA
One reason that I have seen brought down is said in the name of the Chazon Ish. The Chazon Ish held that Tzitzis are only obligated on a "Beged," meaning a garment being worn that gives the normal benefit of a Beged, meaning it benefits the wearer. However, if a person would not have "Beged benefit" from the Beged, it would not be a Beged that is obligated in Tzitzis. Accordingly, a Talis must give such benefit in order to be obligated in Tzitzis, and therefore cannot be said to just be worn to do a Mitzvah without giving the benefit of a Beged. [This reason was quoted in a Kol Torah journal as one of the reasons that is said over regarding why the Chazon Ish did not wear woolen Tzitzis in the summer. According to this reason, he held that to wear an added woolen garment in the Bnei Brak heat does not give any Beged benefit, and it is therefore not a Kiyum of Tzitzis.]
All the best,
Yaakov Montrose