From our perspective at the beginning of the 21st Century it is difficult to see how anyone could have ignored implications of the 3-Dimensional arrangement of atoms within molecules. At the same time it is remarkable that anyone whose only tools were elemental analysis, visual observation of bulk chemicals, determination of melting and boiling points, and the like could possibly have figured out how atoms were arranged.

The pieces began to fall into place in the 1860s and 1870s, soon after Couper and Kekulé suggested the tetravalence and self-linking of carbon. Generally the breakthroughs came from relatively young chemists, because they were less cautious, and less steeped in tradition, than their teachers.

Two significant examples are Koerner's proof of the "equivalence" of the six carbons in benzene (and his subsequent identification of the ortho, meta, and para isomers of disubstituted benzenes) and Paternó's erroneous identification of rotational isomers of 1,2-dibromobenzene. Both of these contributions came from the chemical laboratories in Palermo, on the north coast of Sicily, in 1869, when Koerner was 30 years old and Paternó 22.

The reason these contributions came from such a seemingly out-of-the-way place is that nine years earlier, in 1860, Stanislao Cannizzaro, a 34-year-old Sicilian who had been a chemist in exile since serving in the artillery in an 1847 Sicilian revolt, had returned thirteen years later with Garibaldi's army to help liberate Sicily from the rule of the Bourbon kings. Just months before returning to revolutionary Sicily, he had made his most noted contribution to chemistry - convincing his fellow chemists that gas densities and Avogadro's (and Gay-Lussacc's) hypothesis would give sensible atomic and molecular weights. He convinced them by circulating an outline of the beginning chemistry course he was offering at Genoa in the Kingdom of Piedmont in north Italy. Soon there was no more uncertainty about whether the atomic weight of carbon was 6 or 12, oxygen was 8 or 16, etc. In 1861 was made director of the proposed University Chemistry Laboratory in Palermo, and he began gathering colleagues and students who were as revolutionary in chemistry as in politics. He wrote laudatory introductions for the papers of Paternó and Koerner. He was also very active in teaching (including advocating higher education for women), and community service (municipal council, commissioner of public health, etc.). In 1870 he left Palermo for Rome to serve as Senator (and ultimately Professor of Chemistry). He had married an Englishwoman, and spoke English well, but in 1872 when he was invited to deliver the prestigious Faraday Lecture to the Chemical Society in London, he found himself in an awkward position and again appealed to his teaching,  as he explained in the introduction to this lecture:

Stanislao Cannizzaro in 1858

Gentlemen,

When I received the flattering invitation to appear before you this year, for the purpose of delivering the Faraday Lecture, I found myself in a state of mind, and in circumstances, as unfavoruable as possible to the discharge of a duty so onerous as that of speaking before a learned and dignified auditory like the Chemical Society, and, moreover, in a foreign language, to which I am not much accustomed. With regard to new researches, I had no definite result to communicate which appeared worthy of your attention; and I was at the same time on the point of abandoning my laboratory, my books, and my ordinary way of life, and suspending my studies, for the sake of going to Rome to take part in parliamentary business, and devote myself to long and fatiguing labours, with the view of arranging, and obtaining the means of establishing, a new chemical laboratory in the Eternal City.

Nevertheless, your kindness in thinking of me, imposed on me the obligation of accepting your invitation; and I fortunately called to mind a subject which the celebrated French chemist, Dumas, had promised to treat in 1847, and had thought worthy of occupying the attention of a learned body, like the Academy of Sciences at Paris, namely, the form which, under existing circumstances, should be given to the theoretic teaching of chemistry...

If we are sometimes obliged to talk of the relative postions of the atoms in the molecules, and even to give graphic representations of these positions, we must hasten to remark that these figures are nothing but artifices of the mind, intended to represent to the sight that which in reality we perceive only through the veil of transformations; but that we do not really know what it is that corresponds to that which we call position, either in space, or in the mutual actions of different portions of matter.

The observations do not, however imply any blame of the conduct of philosophers who imagine and try various hypotheses, pushing them even to their utmost limits. The do what they ought to do for the elaboration of the science. But investigation is one thing and teaching is another; and the teacher should beware of petrifying the minds of his pupils by doubtful and transient hypotheses.

...our mistake is not that we take our theories too seriously, but that we do not take them seriously enough...Even worse, there often seems to be a general agreement that certain phenomena are just not fit subject for respectable theoretical and experimental effort.