Anthropologists have long debated whether the customs of a culture invariably function to preserve it.
Conclusion
If it's correct to define culture as the totality of customs practiced by those whose culture it is, then the customs of a culture necessarily function to preserve it, even if just in a trivial sense.
Evidence (because)
Under this definition of culture, if a culture were to abandon any custom, then by definition it would destroy that culture.
Evaluate
This author is making a weird, nerdy argument that will make nerdy logicians snap their fingers in nerdy approval.
Anthropologists are debating whether the customs in a culture help to preserve that culture. (i.e. does celebrating Thanksgiving help to preserve American culture?)
The author is not engaging with the substantive truth of whether customs are a way of reinforcing and solidifying cultural identity. Instead, the author is interested in just making an observation about what is technically true, in a vacuous sense.
Suppose you define a culture as .
Culture X does customs A, B, and C. Culture Y does customs A, B, and D.
Even though they have customs in common, the totality of ABC is different from the totality of ABD, so according to this definition they are each different cultures.
The author's cute observation is that if Culture X were to drop custom C, then they would only do customs A and B. Thus, they would no longer be Culture X, since that culture was defined as the ABC set of customs.
A culture with an AB set of customs is different from a culture with an ABC set of customs. Thus, getting rid of custom C made the group that used to be Culture X no longer be Culture X.
Abandoning that custom destroyed their status as Culture X, so, technically, having custom C preserves Culture X.
Goal
We're being asked about the 2nd sentence. This provides a definition of "culture" as "unique set of customs" so that the author can make her cute mathematical argument.
We could maybe call it a premise, because the author is definitely using it in tandem with the final claim in order to derive the conclusion. But it feels like we could also call it a background claim that the author just scoops up and says,
The answer will probably sound relational (not as simple as premise / conclusion / background / opposing) and convey the idea that the author is just saying, .