From Webster's Dictionary, a non sequitur is "a statement that does not follow logically from or is not clearly related to anything previously said."
Here's a prime example...from London Telegraph:
Headline:
"Climate change poses a “real and present danger” to the immediate health of millions of people, Andy Burnham, the Health Secretary, has warned."
Article Content:
"His comments came as a series of reports suggested that tens of thousands of lives a year could be saved in Britain alone by cutting greenhouse gas emissions."
How?
"Cutting animal farming by a third could significantly reduce emissions and save around 18,000 lives a year in Britain because of the resultant drop in cases of heart disease if people eat less red meat, scientists estimate."