Woolly means made from the coat of a sheep, or vague. A woolly jumper, woolly thinking, a woolly answer.
The figurative sense is a real criticism: woolly thinking is unclear rather than wrong, and it is harder to argue against for that reason. Americans spell it wooly with one l. A woolly is also the jumper itself, in British use.
1adjectivewoollyMade from the coat of a sheep.
“My grandmother knitted me a thick woolly hat for the winter.”
2adjectivefleecySoft, thick and slightly rough to the touch, like wool.
“The lamb's coat was still woolly and warm from the barn.”
Too few real examples of this word to estimate which sense is commonest.
Wool plus -y. Wool is Old English wull, from a Germanic root shared with Latin lana.
Middle English
wolly
English, today
woolly
From Middle English wolly, equivalent to wool + y. Cognate with stq wullich (“woolly”), Dutch wollig (“woolly”), German wollig (“woolly”), Swedish ullig (“woolly”).
Etymology from Wiktionary, CC BY-SA