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Source: p 206, A Little History of Philosophy (2011 ed; not 2012 Reprint ed.) by Nigel Warburton PhD in Philosophy.

  It may seem obvious to you that when you are in pain and you speak about it what you are doing is using words which name the particular sensation you have. But Wittgenstein tries to disrupt that view of the language of sensation. It’s not that you don’t have a sensation. It’s just that, logically, your words can’t be the names of sensations. If everybody had a box with a beetle in that they never showed to anyone, it wouldn’t really matter what was in the box when they talked to one another about their ‘beetle’.
[1.] Language is public, and it requires publicly available ways of checking that we are making sense.
When a child learns to ‘describe’ her pain, Wittgenstein says, what happens is that the parent encourages the child to do various things, such as say ‘It hurts’ – the equivalent in many ways to the quite natural expression ‘Aaargh!’ Part of his message here is that we should not think of the words ‘I am in pain’ as a way of naming a private sensation. If pains and other sensations really were private we would need a special private language to describe them. But Wittgenstein thought that idea didn’t make sense. Another of his examples may help explain why he thought this.
  [...] [I omitted this paragraph on Wittgenstein's example where a man writes 'S' for a special, but nameless, tingling sensation.]
 [2.] The point he was trying to make with his example of the diary was that the way we use words to describe our experiences can’t be based on a private linking of the experience with the word. There must be something public about it. We can’t have our own private language.
[3.] And if that is true, the idea that the mind is like a locked theatre that no one else can get into is misleading. For Wittgenstein, then, the idea of a private language of sensations doesn’t make sense at all. This is important – [4.] and difficult to grasp too – [5.] because many philosophers before him thought that each individual’s mind was completely private.

  1. The appearance of 1 and 2 as too obvious suggests my neglect of something: what exactly?

I know that Antique peoples worked on extinct languages; so did no one conclude 1 and 2 before Wittgenstein? 1 and 2 obviously explain why extinct languages are difficult to comprehend (because extinct languages lack living speakers with whom subsequent linguists can check meaning); was this not obvious to a linguist in Ancient Greek studying Phrygian?

  1. About 4, what exactly was difficult to grasp?

  2. About 5, how did earlier philosophers not conjecture 3 (which appears to me an obvious, reasonable conjecture) that follows from 1 and 2? I know about the controversy of the Sapir-Whorf Hypothesis (if this pertains to 3).

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  • I think it might help to grasp when Wittgenstein was doing philosophy to get this. One corollary of the logical positivists work was something that took language away from its common meaning.
    – virmaior
    May 10, 2016 at 2:25
  • The criticism of W is directed towards the (old) philosophical idea that language express ideas or meaning which in turn are "mental" facts. For (the "second") W, there is no meaning outside communication, i.e. outside the "social" and public use of language.
    – Mauro ALLEGRANZA
    May 10, 2016 at 7:58

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Maybe you are missing that he is not only talking about "natural languages".

If you are thinking of language in therms of etymology, grammar, pronunciations etc. then it is obvious that it is a public affair.

Wittgenstein was rather thinking about it in terms of concepts, truth and falsity and its capabilities of expressing thought in general. His so his definition of language is encompassing, for example, formal languages, or people's internal stream of consciousness.

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