To get at this question, we have to reflect on the goals of the analytical philosophy movement that Wittgenstein was drawn into. Analytic philosophy of Bertrand Russell's day was trying to find a grounding for philosophy in the empirical world, mostly by constructing a math-based system of logic that he thought mirrored the kind of logic used in the natural sciences. The movement was targeted against rationalist philosophy — the kind of deeply inner-reflective argumentation we see in European philosophers, like Hegel, Heidegger or Sartre — and with that in mind it tried hard to establish clear relationships between statements of logic or philosophy and real-world objects or contexts that the statements refer to, or denote. And so we find Wittgenstein, at the end of the Tractatus, saying:
6.53 The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science,
i.e. something that has nothing to do with philosophy: and then
always, when someone else wished to say something metaphysical, to
demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the
other — he would not have the feeling that we were teaching him
philosophy — but it would be the only strictly correct method.
7 Whereof one cannot speak, thereof one must be silent.
So at this stage in his thinking, Wittgenstein has reduced philosophical language to statements that can be expressed in the form — the language — of the natural sciences, and rejects every other kind of statement as non-philosophical.
As you can see, the entire analytical philosophy perspective was inherently linguistic from the get-go, but the intention was to provide what Popper would later call 'demarkation': a systematic way of pushing off statements that were not considered properly philosophical, i.e., those that are irreducible to mathematical logic. However, this approach produced a number of now-famous paradoxes: Russell's paradox, the morning-star/evening-star paradox, etc. These paradoxes pointed out a weakness in the analytical philosophy approach, in that it assumed (and in fact insisted on) clear one-to-one denotation. Ambiguous denotation — referents in statements that had unclear, abstract, or variable objects — create problems for the underlying mathematical models that the movement wanted to invoke.
Russell and most of his cohort kept trying to dig into math and logic to shore up or resolve this difficulty — you can see that in Wittgenstein's quote above, which comes from his earlier work — but Wittgenstein eventually embraced this not as a problem of math, but as a problem of language itself. He decided to reconstruct the act of denoting as a functional convention of human interaction, not an objective feature of the world, and that drew him straight down the rabbit hole into deep language theory.