Counters have always been a stumbling block for me in SE-Asian languages. The best I've managed to come up with relates to the Chinese influence on many of these, and relates to some things I've found in self-study but was never officially taught. So, don't quote me on this, don't cite me in wikipedia, and feel free to correct me if I'm wrong:
- The same syllable can act as both a noun and another part of speech, as a sort of attributive word. (Let's stick with goats: 羊 is the hanzi for goat/sheep.)
- It's "preferable" for nouns to be two syllables. Not a hard-and-fast rule, but a very common trend.
- Certain markers help indicate that this is the "noun-usage" of the syllable, instead of as an attributive word or an alternate reading.
So, 羊 is the concept of goat, or talking about goats in general. But what if you need to talk about specific goats? That's where "counter+word" helps satisfy the two-syllable trend, and cement the noun-ness of the thing and clarifies that it's specifically the item or object or creature itself, as opposed using the syllable as a descriptor. So, with the counter 只 for animals, if you want talk about a tangible quantity of "the living creature that jumps on things and chews on paper and headbutts people," you say that it's 只羊("animal: goat"), as opposed to, say, 羊肉 (goat meat).
So dê alone is the "idea" of goat to indicate goat products, or things attributed to goats--Google Translate suggests sữa dê for goat's milk, and thịt dê for goat meat--but adding con in front of it adds the specification of animal, so con dê gives that "animal: goat" meaning again.
(edited comment for spelling:) From what I have read in Duolingo site's tips and notes and the https://duome.eu/ it is better to thinki of mot, cai, etc as classifiers. See more under the Animals 1 for example, and more and more taught in later lessons, even under questions. There are even cases when classifiers are not needed but those sentences give special meaning to the noun or its sentence. Wrote my comment here on 2020 March 4.
Classifiers are used as a definite article or when counting something. So, it is used for THE goat, and a/1/2/3/10 etc. goat(s). If you are talking about goats in general, like 'goats like to eat grass' then the classifier is optional. (like if you look back in the earlier exercises "báo và tạp chỉ" allows newspaper and magazine as well as newspapers and magazines.
There is more to it, but I think this is a good starting point.
There always coincidences in life, but who knows who might have shared words with each other over the centuries. English for example uses sheriff borrowed from Arabic. Rodeo borrowed from Spanish. And a few curse words from the Anglos and Saxons. For me this type of thing is the fun of learning other languages.