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.
Conclusion
Passengers are safer on a major airline than the new low-fare ones.
Evidence
Major airlines have long-standing records reliably indicating their level of safety. New low-fare airlines have had few, if any, accidents, but they haven't been around long enough to have a reliable record of their safety.
Evaluation
Is there a way for us to argue that the low-fare airlines are at least as safe as the major airlines? There's no way to reliably know that a new airline is safe (since they don't have long-standing records), but maybe there are some major airlines that have a long record of being unsafe, and so taking a chance on a low-fare airline could actually be safer than buying a ticket from a major airline with a history of accidents. All the author said is that the major airlines have records that reliably indicate their degree of safety, but these records may indicate that a major airline has a low degree of safety.
The other direction we could take, since this argument is based on a comparison, is to think about what meaningful differences might exist between low-fare and major airlines that could impact safety. For example, if new low-fare airlines have state of the art collision-avoidance technology that major airlines don't have, then we have some reason to suspect that low-fare airlines might be at least as safe, even if we don't have the records to back it up.
Goal
Look for something saying, or something saying .