The first thing that we need to do is to make a distinction between the redundancy theory of truth, which is a claim about the use of the predicate ‘is true’ in a natural language, and deflationsim, which is a metaphysical claim about the nature of the property picked out by ‘is true’. Usually what you find is that people just use ‘minimalism’ and ignore this difference though they seem to think that redundancy is true and so therefore deflationsism is true (Blackburn is a classic example of this).
The main motivation for redundancy is a collapsing of the meaning/use distinction that is characteristic of Horwich and other neo-Wittgensienians. If the meaning of a word just is the way that that word is used, the function it conventionally plays in a public language game, then finding out how people use the truth predicate and abstracting the rule that defines its function (the T-schema) is finding out the essence of our concept of truth. But there are reasons not to conflate meaning and use (which I won’t go into here). While I do think that people often use the word ‘true’ as a way of communicating that they agree with either what they themselves, or someone else, has said this communicative use of the predicate ‘is true’ depends on its having the correspondence meaning. ‘True’, the English word, means something like ‘being in accordance with the actual state of affairs’ and so it is easy to see how I could use it to express agreement with what has already been said; to say that something is true is to say that it is really the way things are. So in conversation I am able to exploit that meaning in order to indicate that I agree with something that has been said, I am in effect saying ‘yes, that is in accordance with the facts’.
We exploit the meanings of words in this way quite often. Searle (Searle 1969/2001, p. 142) pointed out a similar phenomenon with ‘promise.’ Suppose a parent says to their lazy child “clean your room or I promise I will take away your cell phone!” It is very odd to think the parent is actually promising to do anything here since the thing promised is not something that the child wants the parent to do. In fact this kind of utterance is most likely a threat or a warning. Or consider a professor confronting a student suspected of plagiarism. The professor says “this passage is taken from Wikipedia” and the student says “I didn’t plagiarize! I promise I didn’t!” This doesn’t look like a promise either, how can you promise that you did not do something? This is rather an emphatic denial of the professor’s accusation. How is this possible? It is because the verb ‘to promise’ is one of the strongest indicators of commitment in the English language, and so we adapt it in these cases as a way of indicating that we are really committed. It would be very hard to explain, from Horwich’s view, how the predicate came to have the function of indicating agreement in the first place without appealing to the correspondence meaning that the word has. If this is right then one of the motivations for accepting deflationsim about truth falls apart.