Why did Peter keep going through the whole prophecy instead of stopping at the already-fulfilled part?
Peter kept going because he did not know there would be a 2,000-year interval, the age of grace, between the fulfilled and unfulfilled parts. Still on covenant ground, he expected the whole prophecy to unfold one thing right after another and could not insert a break.
Les teaches that Peter kept quoting the whole prophecy because he did not know a break existed. Jesus, by contrast, in Luke 4 read from Isaiah 61 and stopped in the middle of the verse, saying it was fulfilled before their eyes, because the rest would not occur for 2,000 years. Peter, still on covenant ground and claiming Abraham's promises, could not put a break between verse 29 and 30. He quoted the entire portion as though everything would happen sequentially. The Old Testament program in Psalms 2 showed Christ's coming, rejection, ascension, tribulation, and Kingdom, with no hint of a 2,000-year break. The first half of such prophecies was fulfilled at His first coming; the second half still waits. Peter had no idea of the 2,000 years of the age of grace, so he continued the whole prophecy.