Fire doors in fire resistance-rated assemblies must have a fire protection rating proportionate to the rating of the assembly they protect. According to NFPA 80, Standard for Fire Doors and Other Opening Protectives, and NFPA 101, Life Safety Code:
For a 2-hour fire resistance-rated assembly, the fire door protecting an opening (like a refuse chute) must have a minimum fire protection rating of 1½ hours (90 minutes).
The reduced rating for the door (relative to the wall) is allowed because doors are tested to prevent fire spread through openings for their specified rating period.
½ hour (A) and 1 hour (B) are insufficient for a 2-hour assembly.
2 hours (D) exceeds the requirement but is unnecessary unless specified for high-risk openings.
Reference:
NFPA 80, Table 4.2.1.1: Fire door ratings based on fire resistance-rated assemblies.
NFPA 101, Section 8.3.4.2: Fire door requirements for vertical openings like refuse chutes