Reagan claimed that the in the future, the space program would be not only much safer, but also a source of pride despite all the mishaps from Challenger.
His claimed is absolutely credible and supported by logical, since the empiric evidence shows us that sacrifices and adversities are romanticized throughout history. Not only that, explorers and inventors tend to be exalted in future generations. Columbus is still talked about and so will be Neil Armstrong for stepping on the moon.
In addition to that, it is noted that technology evolves faster every year and safety goes along with it. Cars, for example, are much safer with better break technology and airbags, for example. Space exploration, even though it is still being perfected, is so much safer today than it was when it all started and will be much safer in the future.