Explanation

A hasty generalisation draws a general rule from a single, perhaps atypical, case. It is the reverse of a sweeping generalisation.

Example

(1) My Christian / atheist neighbour is a real grouch.
Therefore:
(2) Christians / atheists are grouches.

This argument takes an individual case of a Christian or atheist, and draws a general rule from it, assuming that all Christians or atheists are like the neighbour.

The conclusion that it reaches hasn’t been demonstrated, because it may well be that the neighbour is not a typical Christian or atheist, and that the conclusion drawn is false.