Travel agent: Although most low-fare airlines have had few, if any, accidents, very few such airlines have been in existence long enough for their safety records to be reliably established. Major airlines, on the other hand, usually have longstanding records reliably indicating their degree of safety. Hence, passengers are safer on a major airline than on one of the newer low-fare airlines.
The criticism to which the reasoning in the travel agent's argument is most vulnerable is the failure to consider the possibility that long-standing and reliable records documenting an airline's degree of safety may indicate that the airline is unsafe.