“Attorney” is the noun, “General” is an adjective, in this case.
We could call attorneys general “general attorneys” (the attorney tasked with representing the legal interests of a sovereign entity in all matters) and it would mean the same thing.
But we wouldn’t call them “generals attorneys,” any more than you would see a group of shaggy dogs and say “look at those shaggies dogs”
“Attorney General” is an example of a postpositive adjective. Postpositive adjectives follow the nouns they modify in accordance with Romance syntax rather than Germanic syntax that English normally follows. They’re usually found in English as a remnant of Norman French influence during the Middle Ages, especially right after the Norman Conquest.
French legal phrases, syntax and all, were adopted into English unchanged, even though in English adjectives almost always precede the nouns they modify. A few examples of legal phrases with postpositive adjectives: accounts payable, accounts receiveable, attorney general, condition precedent, condition subsequent, easement appurtenant, fee simple, president-elect, court martial, queen regnant, heir apparent, body politic, sum total, notary public.
(Source: Bryan E. Garner, A Dictionary of Modern Legal Usage 424-425 (1987).)
However, you would in Spanish. In Spanish adjectives get assigned the number and gender of the noun they modify (though not all adjectives have separate gender forms/spellings) Abogados generales (attorneys generals), with attorney as the noun) would be a literal translation, though I don’t know what Spanish speaking countries actually use that as a title.
My understanding was that it originally wasn’t - it was an adjective that modified “Officer”. A “General Officer” was one who could pretty much be assigned authority over anything and had general authority over all subordinate officer types, while a Colonel or a Lieutenant was restricted in what they could command, e.g. a Lieutenant might not be allowed under military laws or regulations to be placed in command of a full regiment or a whole base. Can anyone find a cite?
Similarly, in the case of Governors General, the French is gouverneurs généraux, with a plural marker on the adjective. Of course in English we have no way to mark an adjective as plural in the same way.
The abbreviation becomes the noun. Maybe not entirely logical, but practical. Of course, you could always insist that everybody call them BIRs. Then start a morale-boosting campaign for your team: Beers for BIRs.
Once we refer to it by the initials, it loses that part of the grammar. Ditto for MREs or POWs. Some plural abbreviations omit the s entirely, because they’re never used in the singular: MPG, RPM.