What are debates about mereology about?
If meaning is largely determined by use and inferential connections, then if a word is used very differently in two groups of people and if the two groups accept very different inferential connections, then the word does not mean the same thing in those groups.
On this account, mereological nihilists don't mean the same by mereological vocabulary as I (a universalist) do: they reject all ordinary examples of parthood, overlap etc.; they reject some of the most central theoretical principles governing these notions; and they ask unintelligible quesions, like:
... is it really so obvious that the bricks [in the house on the corner] compose a single thing? Can you point to something in the perceptual scene which indicates, not just that the bricks are arranged house-wise on the corner, but that, in addition, composition has taken place in this case? (Dorr & Rosen, "Composition as Fiction", p.158)
To me, that makes as much sense as asking me to provide evidence that self-identity 'has taken place' on a particular occasion.
So mereological nihilists lack my concept of parthood (and I lack theirs, presumably). We don't disagree about mereology, we're talking past each other. But perhaps I don't want to say that we mean different things with almost all our words, e.g. with our quantifiers. After all, we use them in almost the same way, we accept almost the same inferences, and so on. So there might be a substantial disagreement between nihilism and universalism, but it is not about parthood or composition. It is about the number of things there exist in certain possible situations. Perhaps it is also about whether people and table and houses exist, and whether there exists anything large enough to be visible to the human eye. I say yes, they say no.
Well, I hope they say no. Like most philosophers who advocate outrageous positions, nihilists will say that we aren't really totally wrong when, in everyday situations, we contradict their positions all the time: when we say that there is a house, we're taking losely; what we mean is that there are atoms arranged house-wise.
But this is a fine line to tread. A nihilist who accepts as true that there are people, houses, tables and other composite objects, is not a nihilist at all. At best, she believes that all our sentences can be given truth-conditions that don't mention composite objects, or that all truths supervene on (partly plural) truths about mereological atoms. But that's something even I could accept (unless there is gunk).
But insofar as nihilists seek to specify the meanings of sentences apparently about tables, etc., in terms of entities that do not commit them to composite objects, they are doing something that universalists cannot accept. It is not clear, however, to what extent they do this since it is not clear to me what exactly is supposed to be preserved in a paraphrase.
I doubt, however, that nihilists can even get the truth conditions right. Plurals aren't enough (consider an example from Gabirel Uzquiano: 'some computers communicate only with one another'). In which case, universalists are free to disagree with nihilists over truth conditions. It would be bad for nihilists to respond by saying that the problem sentences are false, but this does not tell against their account because they are using a special notion of 'part'. etc.
Finally, I doubt the claim about meaning. I think that if universalists and nihilists are both intending to speak English (or German or whatever) when they use 'part' or 'compose', rather than using them as merely technical terms, then universalists and nihilists mean the same thing by 'part', etc., even if one or both parties turn out to be deeply mistaken about parthood and composition.