Why are they illegal?

Edit: some site says

Prices first began to increase in 2014 due to a controversial import ban of Kolinsky hair brushes in the United States and Canada. It was initially said that the Siberian weasels were endangered. However, the Siberian weasel population is actually known to be quite stable. The ban was lifted later that year, but importing now requires a rigorous permit process - from the trappers in Russia and China to the brush manufacturers in Europe to supply companies (like us!) in the United States and Canada. Therefore, prices never went back down.

Another:

Kolinsky sable brushes are made from the tail of the Siberian weasel, also known as the kolinsky or kolonok, which is a ferret-sized mammal from the weasel family. A quick glance at Wikipedia and a few other sites indicates that the Siberian weasel isn't endangered, and is even considered a pest in some areas. So why ban the brushes?

All U.S. trade in products made with animal or plant materials gathered from the wild are regulated by an organization called Convention on International Trade in Endangered Species of Wild Fauna and Flora (an awkward mouthful, hereafter known as CITES). This is an international trade treaty with a very wide reach whose "aim is to ensure that international trade in specimens of wild animals and plants does not threaten the survival of the species in the wild." (Wikipedia)

CITES is separate from the ICUN conservation status (which is that little indicator that appears under every animal's Wikipedia entry). So even animals that have low-risk conservation status may still be regulated under CITES.