It's not so much what he says, as that he says it. So much of modern culture - I suppose this has always been the case - consists of passing tokens backwards and forwards, and rearranging them, without considering whether those tokens have any value in themselves. Strawson is more generous than I am on this point:
'How did the narrativist orthodoxy arise? I suspect it is because those who treat it as a universal truth tend to be profoundly narrative types themselves. They control the current discussion, and assume that the way things are for them is the way they are for everyone else.'
An interesting example that he discusses is the view that we rewrite the narrative of our lives to cast ourselves in a good light. For example, Nietzche: 'I cannot have done that, says my pride, and remains inexorable. Eventually memory yields.'
As Strawson says, people do revise their memory of their past conduct. Some do it a lot. Perhaps we all do it more than we realise. But memory does not always yield. The truth - I did do that bad thing. I did think those selfish thoughts - remains with one. Even if the memory fades, the past is not itself rewritten, and its consequence exists in the present.
And this, I think, is the central issue. There is a truth out there, and it does not yield completely to our verbal tokens. The modern humanities deny that substrate of truth, and say that all that exists is our narrative. My cynical view is that the appeal of this view is that is exempts them from going out into the world and seeing what it is like. It protects them from the truth. But the facts keep coming back at you.