First, he simply asserts and provides no evidence or justification that we primarily learn sentences rather than words. While we obviously hear and read words in linguistic context, normal speech has no explicit auditory divisions whatsoever until we have learned to separate phonemes, words, and sentences through other means. We know from psychological studies (subsequent to Quine's work) that we can learn to separate spoken words of an unfamiliar language passively, merely through sufficient exposure to the language, via the brain's implicit statistical learning processes. Given that sentences themselves rarely recur, whereas words usually do, there is no basis on which to justify the assertion.
This does not mean that the sentential context does not provide information about the meaning of words, or that Quine's idea that the sentences we know or believe do not form a knowledge fabric. But the problem he is attempting to address is one of the validity of theories and the meanings of theoretical terms, not the psychological processes by which we obtain linguistic semantics. Indeed his description of how sentences push and pull in mutual representation, and vary with usage and context is insightful. It anticipates Landauer's theory of Latent Semantic Analysis (Landauer & Dumais 1997), whereby word learning operates via global semantic adjustment through a fabric of interconnected meaning. Ironically, Quine's concerns (from later chapters) regarding the inscrutability of reference are one of the key targets in this seminal paper.
In any case, beyond the emphasis on sentence as opposed to word learning, Quine seems to have a distinctly behaviorist view of how language is learned. Behaviorism was of course quite in vogue at the time he was writing, and it was likely a paradigmatic foundation for most discussions of psychology. Surely in the very earliest stages of a child's linguistic development, there is some repetition, reward, and rebuke involved. However, within a few months of beginning to learn language, a child begins to understand language in general, and entirely different processes enter in.
In particular, a child learns that things have names, and in combination with natural abilities to notice, remember, and group similarities in perceptual stimuli along with motivational elements such as emotional significance or perceptual distinctiveness, the child can perform the earliest elements of conceptualization without direct assistance or any sort of social reinforcement. He might even assign a temporary neologism or perhaps an exemplar/memory-based reference to the object, culminating in the question "what's dat?" The answer, which is the only social contribution, is remembered, and the word is now assigned to the representation via a single training example. It does not need to be reinforced.
Of equal concern is the emphasis only on the formal representations of knowledge without consideration of the underlying psychological semantics, including memories of particular exemplars, syntheses of exemplar qualities (both perceptual and otherwise), informal contextual links (e.g., those two words were both learned when I was hungry - perhaps coincidentally and perhaps not), and emotional valence. A word brings to mind all these things, not just the object of reference, and the fabric of connections among words and concepts operates through these elements as well as directly through the words (contra Landauer as well). Models like those of Barsalou (Barsalou 1999) that have amassed considerable evidence illustrating how non-symbolic representations that co-activate in the brain (called "simulations") push and pull and both contribute to learning and provide a great deal of semantic content.
In short, while Quine's approach may provide important insight into the formal propositional structure of theories and knowledge, his forays into developmental psychology are found mostly wanting.