The linguist mentions that some people have interpreted certain studies as showing that bilingualism overstresses children's linguistic capacities and thus causes them to have a smaller "conceptual map". This is because these studies, which gave vocabulary tests to bilingual children, apparently showed that these children have a smaller vocabulary than most of their peers.

But the linguist points out that these studies are flawed, since the tests were administered in only one language, while dual-language tests have shown that bilingual children often express a concept with a word from only one of their two languages. In other words, bilingual children's "conceptual map" may not necessarily be smaller. It might just be "spread out" across two languages, and the single-language vocabulary tests would fail to show that. Thus, the linguist significantly undermines the evidence for the other people's claim that bilingualism reduces the size of children's conceptual maps.

The linguist undermines the opposing argument by pointing out a major flaw in the evidence for that argument. If the vocabulary tests in the studies were only administered in one language, they likely revealed only part of bilingual children's conceptual maps. Bilingual children might be aware of other concepts, but only be able to express them with vocabulary from their other language. This undermines the view, based on these studies, that bilingualism somehow reduces children's conceptual maps.

Note that while the linguist's argument strongly weakens the opposing argument, it doesn't necessarily defeat that argument. It could still be true that bilingual children have a smaller conceptual map than their peers, even accounting for both of their languages. But by exposing this flaw in the studies, the linguist reveals a major problem with the only evidence mentioned for the opposing argument. Even if the opposing claim turns out to be true, those arguing for it would have to use different evidence to show that it is true.