The an in an bainne sin combines with the sin to give you "that milk", rather than "the milk sin". In the case of é sin, you aren't specifying what "that" refers to in English, you don't say "that 'it'", but the pronoun é takes the place of a noun like an bainne.
The inconsistency is really in English rather that Irish.
It could be from a number of Germanic languages, as Ungewitig points out below. If it were, though, I would expect to think of it as characteristic of the Great Lakes and the Upper Midwest. "That there," though, sounds to me more characteristic of the Appalachian region, which was settled early on by the Scots Irish. It's also found in Welsh, of course, but I there was not an immigration of Welshmen to the American colonies or early United States concentrated enough to leave a mark on the language, I think. I wonder if something like this structure occurs in the Spanish of Y Wladfa in Argentina.
i wish this site would give explanations as to why an answer is wrong. Previous question's answer was "is maith leis na buachallí í sin" (the boys like that). i'm wondering why there's an "í" between "buachaillí" and "sin," but not between "bainne" and "sin." Can anyone tell me?
Correct me if I'm wrong, but í refers to it, so for sin to work for that (being an object in itself) then it would have to be used as "it there", just like how that milk would be translated as "an bainne sin" which can also be translated as "the milk there". This is why "Is maith leis (verb) na buachallí(subject) í sin (object)".
and the distinction between broad and slender n is starting at 3:50
For various pronounciations of bainne look below
This sentence is included in "Irish Conjunctions". I presume that the "conjunction" in this sentence must be "sin". In Béarla, which I have taught for many years as an elementary school teacher in the US, its English cognate, "that", can serve as several different parts of speech: Definite Article, Conjunction, Adverb, Pronoun or Adjective. I would like to respectfully suggest that, in this instance, it does not serve as a Conjunction but as a Definite Article.