A brief summary of an article I came across from Aish:
"You shall not wear a garment that is made of a mixture of wool and linen together." (Devarim 22:11) "You shall make fringes on the four corners of your garments..." (Devarim 22:12)
Originally, the Gemara (Shabbos 27b) assumed that the juxtaposition of these two Pesukim means it should be read as follows: "You shall not wear a garment that is made of a mixture of wool and linen...[rather] you shall make fringes on the four corners of your garments [using these materials - wool and linen.]"
This would imply that while normally wool and linen mixtures are forbidden, it's actually preferable to use this mixture for Tzitzit.
However, this is seemingly a contradiction against the Pasuk "You shall place ont he corner Tzitzit blue wool thread." (Bamidbar 15:38) which specifically says wool.
Rava explains how this isn't a contradiction - the Pesukim in Devarim are teaching that if you have Tzitzit strings made of wool or linen, you can fulfill the Mitzvah of Tzitzit with any garment. The Pasuk in Bamidbar is teaching that if the strings are made of any other material, you can only fulfill the Mitzvah of Tzitzit if the garment is the same material.
There begins a complicated Machloket between many Halachic Poskim... I would view the full source to see the argument, but I believe this is the source of the original statement.
Full source here.