Non Sequitur

When a conclusion is supported only by extremely weak reasons or by irrelevant reasons, the argument is fallacious and is said to be a non sequitur. However, we usually apply the term only when we cannot think of how to label the argument with a more specific fallacy name. Any deductively invalid inference is a non sequitur if it also very weak when assessed by inductive standards.

Example:

Nuclear disarmament is a risk, but everything in life involves a risk. Every time you drive in a car you are taking a risk. If you're willing to drive in a car, you should be willing to have disarmament.

The following is not an example: "If she committed the murder, then there'd be his blood stains on her hands. His blood stains are on her hands. So, she committed the murder." This deductively invalid argument commits the fallacy of affirming the consequent, but it isn't a non sequitur because it has significant inductive strength.