Terms for collections of animals

If you really want to understand the naming of animal groups, it might help to classify the types or origins of classification terms. There are words that have simply been borrowed from the past (e.g. an exaltation of larks) or from a particular language, dialect or regional speech. These are often popular among poets.

There are other words that are more commonly used. For example, most people would describe a group of larks as a "flock," not an "exaltation."

Scientists may use still other words.

Some of the most common collective words that I'm aware of are "herd" (generally applied to ungulates, or hoofed mammals), "flock" (of birds) and "school" (generally applied to aquatic animals, especially fishes).

P.S. The term "flock" can indeed be applied to geese and crows.

It was lingual fun.

The trend developed in the middle of the 15th century and one of the first such lists occurs in The Bokys of Haukyng and Huntyng; and also of coot-armuris better known as Boke of Seynt Albans or The Book of St. Albans printed 1486.

That it also contains such entries as "a doctrine of doctors", "a disworship of Scots" and "a gaggle of women", "a sentence of judges" and "a fighting of beggars" shows that this was something people had fun with from the early days of the form.

It provides a form of idle learning; the pointlessness of knowing such collective nouns is where the charm lies. It is telling that such uses largely died away, but made a revival in the 19th century.

Likely they originated in the earlier distinctions of e.g. using flock for sheep and goats but herd for cattle and deer, and was then taken to further lengths.

Wikipedia suggests that the terms derive from Medieval hunting terms. The source cited is An Exaltation of Larks.

Sometimes the collective noun gives you additional meaning or maybe some poetic beauty. But most of the time it doesn't really add much. Most people will understand the phrase "A flock of crows" completely and some people won't even know that they could say "a murder of crows". Then there's the connotation of the word "murder" which you may not even want.

One advantage to using the collective nouns is that the collective implies the type of animal, so if talking about lions and gazelles you could say "The gazelle was overtaken by the pride" and anyone who knows that lions are in a pride would understand what you are saying.

Aside:

The situation is comparable to Chinese, where EVERY NOUN has a measure word. You don't say "two chopsticks", you say "two sticks of chopstick". In English we can say "two beers" but in Chinese you have to say "Two bottles of beer". However, there are lots of cases where a "proper" measure word can be replaced by a less proper one, or the generic measure word (ge 个). If you don't know the word for "small round thing" you can say "two ge marble" if you want two marbles. It's not 100% correct but people will understand and that's the important part.

I very much doubt you there is a definitive answer for this.

Collective nouns became popular in the 14th and 15th century.

There are exhaustive lists. I suspect people considered it more artful and "proper", back in the day.

Animals in groups behave differently; the collective noun often hints at the behavior, formation or character of the group.