I think the confusion for me is more in the word "knit." For me, "knitting" involves lots of spaghetti-sized strands of thick wool or yarn, assembled with knitting needles.

I think other people use "knit" to refer to a much more fine weave, such as might be found in your typical cotton shirt. I've never used that definition of "knit" myself. I think it might be the definition that brian1789 is using here though.

I definitely don't consider "any turtleneck" to by definition be a sweater... for me, a turtleneck would only be a sweater if its strands were of spaghetti-thickness.