Sherem's response to Jacob is only to the second part of Jacob's argument. Sherem abandons his scriptural position in its entirety. Why? Even in this abbreviated form we can get an idea why Sherem would so easily abandon his position. Jacob indicates in verse 14 that Sherem has been convinced by Jacob's exegesis, to the point that Jacob discerns that now Sherem "know[s] [it] to be true."
Sherem's entire position since arriving in the town of Nephi has been based on scriptural argument, and based on a preaching of the Law which established a common ground. Jacob has demonstrated to Sherem, if to no one else, that the scriptures do teach of a Christ. Sherem cannot abandon his position entirely, however.
Sherem probably understands that scriptural argument can be persuasive in many ways, and that he can at least claim a draw with Jacob on scriptural terms. Even though Sherem might understand that he has lost that part of the "debate," it is likely that the less trained among the audience would not know that. Therefore Sherem presses on with his attempt to discredit Jacob, and does so where he believes that Jacob is most vulnerable.
Jacob has left himself open to an appeal to divine judgement because he claimed divine sanction. Sherem calls what he believes to be a bluff. Sherem can use Jacob's claim of prophetic knowledge against him by requiring that Jacob prove the prophetic connection. Sherem therefore asks for a proof, not because he wants one, but because he is certain that Jacob cannot provide one. If Jacob does not provide a proof, then Sherem can deny Jacob's prophetic calling on the basis of lack of evidence, and the denial of the prophetic calling will cast doubt on Jacob's scriptural interpretations.
In this debate of wills and intentions, it is a masterful move. It also fails because Sherem does not believe that Jacob is a prophet. Sherem will discover that he has made a fatal mistake.