“Non sequitur” is Latin. It means: it doesn’t follow. It’s usually used when someone makes an argument to prove something he/she is proposing that doesn’t support that proposal. In the past I’ve been the “king of non sequiturs” and I’m trying hard to lose my title. It’s a question of linkage.
For example I say: “We don’t really know how the ancients got those huge blocks to the top of the pyramids.” You say: “So?” I say: “Therefore they must have been built by beings from outer space.” You jeer at me and speak Latin: “Non sequitur!”
Part of the problem in non sequitur proposals is that the first claim may well be true and we’re fooled by that and don’t notice that the therefore is a lousy link; the truth of the first part doesn’t lead to the claim in the second part.
We hear non sequiturs all the time.
“Natural selection operates in the world therefore there is no God.”
Or: “Scientists can manipulate genes and affect human life therefore God didn’t create genes (or humans).
Or: “Scientists can routinely produce amino acids, the building blocks of life therefore there probably is no God.”
Or: “Scientists can imitate the first seconds after the Big Bang therefore God probably didn’t create the universe.”
Or: “If we spend gazillions of dollars and brain-power on space probes we might find the building blocks of carbon-based life on other planets and that will explain how we got here and it will help us get out of the mess we’re always in.”
You hear this kind of thing from religious people as well.
“In the OT God blessed polygamous people therefore God approved of polygamy therefore God approves of polygamy today.”
“In the OT God gave laws regulating slavery therefore slavery had God’s approval and therefore God would approve of Christians having slaves today.”
“In the OT God gave laws regulating divorce ‘for any cause’ therefore God approved of it and therefore Christians have a right to divorce ‘for any cause’.”
“In the OT God regulated the drinking of intoxicating wine therefore it’s the Christian’s freedom to support the modern booze industry.”
“In the OT God gave “wine” (yayin, oinos) as a gift to mankind therefore he gave intoxicating wine to mankind as a gift.”
“God has given humanity intoxicating drink as a gift therefore the booze industry is doing us a favour by getting it into our hands therefore it's the irresponsible drunks who should be castigated and not the booze industry.”
“In the NT Jesus made barrels of wine (oinos) and shared it therefore it’s a Christian’s freedom to own bars, sell and promote the sale of booze (including whiskey, rum, brandy and the rest).