What underlying semantic notions explain the etymology of 'fustis'?

Question

_{I already consulted Etymonline and Wiktionary.
Source: p 56. The Merriam-Webster New Book of Word Histories (1991).}

  Another word that has undergone a similar development is fustian. In its earliest sense
[4.] fustian is 'a fabric made from cotton and linen', but like bombast it too is now used to mean 'pretentious speech or writing'.
The word itself is from [3.] Medieval Latin fustaneum, whose origin is disputed. One account traces it to [2.] Latin fustis 'club, staff', as a translation of
[1.] Greek xylinon, literally meaning 'wooden' (from xylon, 'wood, club') but applied to cotton.
That such an origin is at least semantically possible is shown by another Medieval Latin term referring to cotton, lana de ligno, literally 'wool of wood'. Such a conception lies at the basis of the German word for cotton to this day, Baumwolle, literally 'tree-wool'. Another account de- rives fustaneum from the Cairo suburb Fostat (Arabic fusṭāṭ), where fus- tian is said to have been manufactured. Even on that route we wind up back at Latin, since fusṭāṭ, literally 'camp', comes (via Greek transmission) from Late Latin fossatum 'ditch, fosse'. See also DENIM.

What underlying semantic notions connect:

5. 1 and 2 (i.e. 'wooden' + 'cotton' to 'club, staff')?

6. 2 and 4?

Answer 1

I can only make educated guesses, mostly about what the quoted paragraph is intended to mean, but these might help.

5. Note that the Greek word ξύλινων primarily means "wooden". Using the word for "wood" for a club comes pretty naturally, since clubs are made of wood. Even in English, heavy (wooden) golf clubs are called "woods". In the connection from "wooden" (ξύλινων) to "club" (fustis), the notion of "cotton" plays no role.

6. As I understand the quoted etymology, it says that people speaking Greek were referring to cotton using the word ξύλινων, by a somewhat inscrutable connection with wood also found in modern German. The hypothesis is, when someone wanted a Latin word for a certain kind of cloth, they thought to do in Latin what had been done in Greek: use the word for "wooden" to mean "made of cotton"; and then make a noun out of it. So, the hypothesis proposes that fustaneum arose from two somewhat strange analogies: first, wood–cotton; second, "Let's do the wood–cotton analogy in Latin analogously to what they're doing in Greek."

Note that the quoted etymology is trying to explain the origin of the English word fustian. It's not trying to explain the origin of the Latin word fustis—the origin of which is not known for sure. Even the origin of the Latin word fustaneum isn't known for sure. The whole thing is awash in uncertainty.