In this case, it is the minor premise that is most open to challenge. If the writer can convince his reader that it is, then the reader will accept his conclusion. This way of arguing is called deduction. When one deduces, she moves from a general argument to a specific argument. The great detective Sherlock Holmes was famous for his deductive arguments.
All watchdogs bark at strangers.
When X was murdered, the dogs did not bark. X was not killed by a stranger. Detectives like Columbo and Kojak might gather their clues from specific observations. From these observations they then determine inductively who the murderer is. It's important to note that many of the major premises used in syllogisms are often arrived at through inductive reasoning.