Jesus gives his testimony that the words of Isaiah will be fulfilled. Although this is implicit in asking them to read Isaiah, it is nevertheless explicitly given as a promise.
“Great Are the Words of Isaiah”
The specific reason for reading Isaiah is that it contains answers to questions that the Nephites are asking. They are interested in the house of Israel, particularly in the gathering. That is a theme in Isaiah, so the Nephites are told to read Isaiah for their answers. Since the Gentiles are involved in those future events, the Savior does note that Isaiah is also of value to the Gentiles.