I'd like to see the numbers, but I imagine that the synthetic textiles chunk comes from the sheer volume of fast-fashion and trashion produced every year. I have synthetic shirts that are well over a decade old and still look and function as brand new. My cotton shirts under similar wear get ratty and frayed in that time frame (and require harsh chemicals for stains).
If we stopped over-washing and over production, I wouldn't be surprised if the lifetime ecological footprint of synthetic garments is less than a cotton equivalent.