The preamble to the major 1997 Part 61 update explains the FAA's position that a CFI is paid for instruction, and is not flying for compensation or hire. The updated regs explicitly say a CFI requires only 3rd class.
Murphy 2008 LOI: a CFI is paid for instruction, and is not flying for compensation or hire -- cites the 1997 preamble -- notes that earlier LOIs Gandy 1991 (flying for hire, needs 2nd class) and Rubin 1991 (not flying for hire, needs only 3rd class) are in conflict, and have been removed from the Chief Counsel's website.
I don't have the links handy, but these can be found online.
Murphy 2008 LOI: a CFI is paid for instruction, and is not flying for compensation or hire -- cites the 1997 preamble -- notes that earlier LOIs Gandy 1991 (flying for hire, needs 2nd class) and Rubin 1991 (not flying for hire, needs only 3rd class) are in conflict, and have been removed from the Chief Counsel's website.
I don't have the links handy, but these can be found online.