Connectives such as but are critical for building coherent discourse. They also express meanings that do not fit neatly into the standard distinction between semantics and implicated pragmatics. How do children acquire them? Corpus analyses indicate that children use these words in a sophisticated way by the early pre-school years, but a small number of experimental studies also suggest that children do not understand that but has a contrastive meaning until they reach school age. In a series of eight experiments we tested children's understanding of contrastive but compared to the causal connective so, by using a word learning paradigm (e.g., It was a warm day but/so Katy put on a pagle). When the connective so was used, we found that even 2-year-olds inferred a novel word meaning that was associated with the sentence context (a t-shirt). However, for the connective but, children did not infer a non-associated contrastive meaning (a winter coat) until age 7. Before that, even 5-year-old children reliably inferred an associated referent, indicating that they failed to correctly assign but a contrastive meaning. Five control experiments ruled out explanations for this pattern based on basic task demands, sentence processing skills or difficulty making adult-like inferences. A sixth experiment reports one particular context in which five-year-olds do interpret but contrastively. However, that same context also leads children to interpret so contrastively. We conclude that children's sophisticated production of connectives like but and so masks a major difficulty learning their meanings. We suggest that discourse connectives incorporate a class of words whose usage is easy to mimic, but whose meanings are difficult to acquire from everyday conversations, with implications for theories of word learning and discourse processing.