I think it is a pretty simple argument to defend against.
No one knows they are different from or identical to God or brahman, because no one knows there is such a thing called God or brahman from everyday experience. "shAstrayonitvAt", says the 3rd brahmasUtra. Brahman can be known only from scripture. When brahman can be known only from scripture, how can anyone know they are same or different from brahman just from everyday experience? Scripture is not purposeless because scripture teaches brahman, which cannot be known from everyday experience. "janmAdyasya yataH", says the 2nd brahmasUtra. Brahman is that from which the origin etc. of the world proceed. It is not a matter of experience that an intelligent entity (called brahman) gives rise to the universe. If that were so, even materialists would have accepted brahman. But they do not.
Let me elaborate this further, since this question got a bounty of 50 points. Here is an imaginary discussion between a dualist and a non-dualist -
Non-dualist: We all know we are different from brahman from everyday experience. If scripture teaches us the same thing, scripture is not adding anything new to our knowledge. Scripture will become purposeless.
Dualist: We dont even know that there is such an entity called brahman from everyday experience. It is precisely because of this reason that there are atheists and agnostics. The purpose of scripture is to tell us that there is an entity called brahman who is the cause of the world etc. So your statement that we know we are different from brahman in everyday experience is incorrect, because we dont even know there is an entity called brahman from everyday experience.
Let me add a bit more to the answer. This time, I want to turn the tables on the non-dualist.
Let us leave brahman out of the picture since that part is already adequately answered above by me in my opinion. The non-dualist is also claiming that we all know we are different beings from our experience. The non-dualist is correct here. Experience shows we are all different beings. Hence scriptural interpretation cannot and should not contradict this experience. There is a well known saying that thousands of scriptural statements cannot make a black crow white. In short, scriptural statements cannot contradict experience. Therefore, thousands of scriptural statements cannot make "you" and "me" the same. The non-dualist argues that "you" and "me" are the same brahman. In doing so, the non-dualist is essentially making a black crow white. (S)he is pitting two pramANas - pratyaksha and shAstra, against each other, rather than bringing out the harmony between them.
Further addition regarding the jeeva to address a point raised in the comments -
Krishna (scripture) says - dehino 'smin yathā dehe
kaumāraṁ yauvanaṁ jarā
dhīras tatra na muhyati (Bhagavad geeta 2.13).
By these statements, Krishna/scripture is pointing out the existence of an immortal jeeva even when these bodies die. Such information, is once again unavailable for perception and happily acceptable to a dualist.