Post Hoc Ergo Propter Hoc

This is a fallacy in which a person thinks that an prior event caused some outcome, simply because it came before.

Examples

Several people looked up into the sky and then pulled out their umbrellas and lifted them above their heads. A few minutes later, it began raining. Therefore, deploying of umbrellas causes rain.

The priest prayed before a battle for the enemy army to be destroyed. In the end, as it happens, the enemy army was defeated. Therefore prayer causes military defeats.

A child got sick. It was said that a witch was doing something odd that looked like magic sometime before that. Therefore the witch put a curse on the child.

A famous lesbian moved to a city, and later a huge hurricane hit a city. Lesbianism causes hurricanes! A prominent American preacher actually made such a claim.

Weaknesses

The arguer is making the mistake of deciding that one prior event, rather than any others, or even a concurrent event, caused the second event or outcome. You should ask: Haven't you considered that something else might have caused B, other than A?

It may be that nothing in particular caused event B. Suppose a die was thrown and the number 6 came up. That's random. Nothing caused it.

Event A could be completely irrelevant, or unable to affect anything. For example, if A is Ten people prayed for Bobby who was ill, you can expect little or no effect, unless Bobby consequently felt some performance anxiety.

It may be, as if often the case, that a complex interaction of events caused the event B. You can attack the simplistic view that only one event caused B.