
Continuity mistake: In the final scene on the bridge, Spock and McCoy are wearing colored arm bands which identify their departments: Spock's is orange (for Science) and McCoy's is green (for Medical). In the very last shot, Spock is wearing the green band and McCoy is wearing the orange one.
Answer: Deltans exude an intensely potent and effective chemical substance known as pheromones, which act as signals arousing an intense sexual reaction in other species (in other ST material it's inferred that its potency is so extreme that a non-Deltan risks insanity in a sexual encounter with a Deltan). Upon entering Starfleet, Deltans must swear "an oath of celibacy" so as not to influence or take advantage of crewmembers. That is why Lt. Ilia stated that her "oath of celibacy" was on record.
Super Grover