The Non-Sequitur

This is a form of Red Herring i.e. distracting tactic, in which two separate claims are put forth and the arguer pretends that one implies the other.

Examples

There is a god because I believe there is a god.

You come to the defense of gays therefore you must be gay.

She's unmarried therefore she must hate men, be a lesbian, be a bitch etc.

The laws are to be upheld because they are the laws.

The child is sick because a witch put a curse on her.

Weaknesses

You need only point out the lack of linkage. One claim does not imply that the other is true.

Sometimes the linkage is not intentional and may be the result of lazy or shoddy thinking, or it may be the mistake of someone who is half-awake. Don't assume a sinister intent; just point out the error.

People of various stripes often use non sequiturs to cast blame or guilt on whatever group they're biased against. They are X therefore they do Y. Often X is not true or not common, and Y is not implied by X anyway. This is a process of piling on guilty characteristics onto a group or individual.

Once the two arguments are acknowledged to be separate, you can attack each separately. Non-sequitur invites a divide-and-conquer approach.