Why do both these cases need to exist?
They are both subjects
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Because they behave differently, and contrast with different things.
In a language like Hittite, some nouns have one case that's used any time it's the subject of a verb, and one case that's used any time it's the object of a verb. This is the system you're probably most used to.
Other nouns, though, have one case that's used for the subject of an intransitive verb and the object of a transitive verb, and a different case that's used for the subject of a transitive verb.
We call those first two cases "nominative" and "accusative", because those are the traditional terms going back to the ancient Greek and Roman grammarians. But what should we call the other ones? Both of them can be used for subjects; it just depends on the type of verb. And neither one acts quite like what we call the "nominative".
So instead we call the third case "absolutive" and the fourth case "ergative". It just makes it simpler to have different terms for them, because they function differently in the language.
(Well, in Hittite specifically, some people prefer the term "nominative-accusative" instead of "absolutive", since it can act like either the nominative or the accusative depending on the verb. But I find this unnecessarily confusing. It's a separate case with its own distribution; just give it its own name.)
Actually, considering the absolutive case as different from nominative is a rather modern development.
We speak of a nominative case when the language in question has nominative-accusative alignment and of an absolutive case when there is ergative-absolutive alignment. When a language has tripartite alignment the subject case is also often named absolutive, but there exists also the term intransitive case.
First, cases don't "exist". They're not natural phenomena that can be discovered; they're categories (like races or curries or kinship systems) that people can use to sort stuff. Different languages have different case systems, with different (and differently-named) cases, or sometimes no cases at all (Mandarin has no case; English has cases only on certain pronouns, and they're fading).
Second, the case systems most Europeans (and therefore Americans, who are European culturally) are familiar with are Indo-European and Uralic, both of which are Nominative-Accusative in category; and (for Vasconists and a few others) Basque, which has an Ergative-Absolutive type case system. As usual, Basque didn't influence much outside its area.
But when Caucasian and Australian and Mayan languages (not to mention split-ergative languages like Hindi and Sumerian) were added to the typological mix, it became clear that Nom-Acc was not the only way to view transitivity. Most linguists in the Early Stone Age started off using Nominative for what I always call the Absolutive, probly on the basis that one strange name was enough. But when I learned about case systems back in the Pliocene, we were careful not to call it Nominative, because that was part of a different system.
So, no, both names shouldn't be used. I prefer Absolutive because it names the right system, so that all the names one might use designate correctly. That's the first requirement. But others prefer their own terminological array. This is normal; there is no Top Boss to determine or defeat.
On the other hand, in 3-role systems of the Austronesian style, there is no settled nomenclature, because the languages have evolved such different ways to deal with transitivity (and its correlate, so-called passives); each has to be considered individually.