The non sequitur is the Latin phrase for “(it) does not follow.” It means that the conclusion reached does not follow the premise or premises.   Non sequitur arguments are hilariously disconnected, but often they can be subtle and may not be easily uncovered.

The arguments are fallacious since they do not provide any evidence for an argument and are just meant to confuse the listener.  

Example of a non sequitur

Syracuse University has a terrible football team. Thus, vaccines are neither safe nor effective.