Why can't the Psalm Peter quoted be about David himself?
The psalm cannot refer to David himself because David died and was buried, and his sepulcher remained to that day. Peter explains David spoke as a prophet, foreseeing that God had sworn to raise Christ from the dead to sit on his throne. The psalm therefore describes Christ's resurrection, not David's.
Les explains that David was not referring to himself; he was quoting Christ, speaking as if Christ had been in those situations. Peter returns to first-person speaking and says that David is both dead and buried, and his sepulcher is with them to that day. David was not saying death could not hold him, because David is dead and buried. But verse 30 says David, being a prophet, knew God had sworn with an oath that of the fruit of his loins according to the flesh He would raise up Christ to sit on his throne. Les points out that the Psalms are loaded with prophecy, just as much as Isaiah and Daniel. Peter is driving at their king whom they crucified: God raised Him from the dead, and He can still be their king. Verse 31 says David, seeing this before, spoke of the resurrection of Christ.