We can't know exactly which quality led so many languages to independently develop or borrow the metaphor — etymological dictionaries rarely speculate on the "why" — but here are my thoughts.
There are at least three qualities of "head" that have a possible metaphor with "chapter".
Head = (most) important. So natural that examples are hardly needed.
Head = first. "Headwaters", "headline", "head off" (get there first), "ahead" (first), etc.
For some cross-linguistic confirmation from an unrelated language, consider e.g. Hebrew Rosh Hashanah lit. "head of the year", translated "New Year's Day". (The root of rosh incidentally appears in many words, including bereshit usually translated "in the beginning").
Head = orientation. "Ahead" (in the direction faced), "head somewhere", "head fake", etc. Perhaps by connection with face (which direction are you facing?).
Let's investigate using the OED. Their etymology is a good example of how we usually ignore the "why" while charting the "how"; nothing here identifies the link used in the metaphor:
Etymology: A later syncopated form of chapiter n., < Old French chapitre, earlier chapitle < Latin capitulum. diminutive of caput head, used, in ancient Latin, in the senses ‘little head, head of a plant, capital of a column’, and later, those of ‘head-dress of women, chapter of a book, section of a law’. The form chapter appears in Scots in 14th cent., but in English is rare before the 16th; chapiter survived beside it till the middle of the 17th, and is still occasional in the sense ‘capital of a column’.
But I think the definitions themselves give us clues that (1) above is the relevant link:
1. a. A main division or section of a book (whether the latter is an entire literary work, or one of the divisions or parts of a large work). Esp. used of the main divisions of the books of the Bible.
There are examples from as early as c. 1000, but this is the earliest one that's unambiguous to me:
c1386 Chaucer Nun's Priest's Tale 245 In the same book..Right in the nexte chapitre after this.
The ambiguity of the earlier examples arises from overlap with this definition:
2. fig. Head, heading, subject, category. (Usually preceded by on, upon.) arch.
A seemingly relevant example:
1681 W. Temple Mem. iii, in Wks. (1731) I. 342 Upon which Chapter I said a good deal.
And one more whose examples are much later but possibly related to the underlying mechanism:
5. c. A branch of an organization or society, esp. of a college fraternity. U.S.
Based on these, we could propose a semantic development along these lines:
(broadening) important thing
(narrowing) among some group of collected items, e.g. people, the representative or chief
(sideways/synecdoche) something having been organized, a main division
(narrowing) a main section of a book
(broadening) any section of a book
The paradox is how a word that means "head" came to mean "subdivision". We have to switch our point of view: Looking at a book, the chapters are subdivisions. But looking at the mass of words, each chapter heads a group of them. The chapters of an organization are branches of the whole, but in terms of the members a chapter collects them under a single head(ing). And again, the world has any number of things that are grouped into the "categories" of definition 2. And not just any sections, but the "main" sections of definition 1c. To start with, anyway.
So a chapter is a "head" not looking from the top down, but from the bottom up.