Actually I can tell you why they call this style "cottage" knitting.
People who knitted for a living worked from their homes -- their cottages. They used this style because it was so much faster than either English or Continental. These people were paid by the completed piece, so the faster they could knit, the more they could earn. Knitting was one of the first "cottage industries"!
English and Continental knitting styles, on the other hand, were used more by the gentry -- people who knitted more for pleasure or just for their family than from the necessity of having to earn a living.
I got this from some book or other many, many years ago and I always thought it was interesting!