Ancient Greek used connecting vowels between two stems when forming compounds, unless the second stem started with a vowel (e.g. nost-os ‘homecoming’ + algos ‘pain’ > nost-algia). A vowel was also unnecessary if the first part of the compound was a numeral or preposition, which instead had their own optional vowels: tetr(a)– ‘four’, di(a)– ‘through’, an(a)- ‘on’, etc. So connective vowels really only apply when the first component of a compound is a noun or verb.
(And in the case of –logia, those formants keep their vowels: tetra-logy, dia-logue, ana-logy.)
Verb-initial compounds are rare in Greek, and even rarer in borrowings into English or novel coinages; they can have any of -e-, -o-, or -i- as a connecting vowel. mis-o-gynist ‘hate-women’ has an -o-, but arch-i-tektōn ‘lead builders’ has an -i-.
Almost all Greek compounds borrowed or newly coined in English are noun-initial. The connecting vowel was not always an -o-; however, it was an -o- much more often than not. The original rules are:
- If the noun is in first declension (ends in -a(s) or -ē(s)), use -ā-: agora ‘market, forum’ > agor-a-phobia
- If the noun is in second declension (ends in –os or –on), use –o-: Angl-os ‘English’ > Angl-o-sphaira, archaios ‘ancient’ > archai-o-logia.
- If the noun is in third declension: by default use –o-; you can skip a connective vowel if the stem ends in a vowel. ichthy-bolos ‘fish-catching’ but ichthy-o-pōlēs ‘fishmonger’ (and hence ichthy-o-logy)
- If the stem ends in –es (or neuter –os), substitute it with –o-: pseudēs ‘false’ > pseudo–
So you’re already seeing that most of the time it’s –o-.
–o– got generalised even further, already in antiquity: first declension nouns could use –o– instead of –ā-, and that in fact happens with techn-o-logia < technē. I presume that in modern coinages, the –o– became universal with first declension nouns, by analogy. So the study of stones could be either petr-a-logy or petr-o-logy; the former is what you’d expect from Ancient Greek petr-ā, but the latter is more frequent in English, because we expect –ology in all such compounds. The third declensions with a bare stem do turn up: brachy-cephalic; but they are quite rare.
So most Greek and Greek-inspired compounds beginning with a noun use –o-, unless the second word starts in a vowel.
The reason why this rule of Greek has become a rule of technical English is because Greek formed compounds much more readily than Latin; so when a compound needed to be put together for a technical term, Greek was the language we reached for.