Why does a red sky at night mean good weather and not vice versa?

Answer 1

It doesn't MEAN good weather; it's just that with the prevailing weather patterns moving from west to east around the world, a "red sky at night" indicates that the skies far to the west are clear and not filled with clouds. So twelve hours later, the sky still ought to be clear. It is more a statistical argument than anything else.

Answer 2

A red sky at night typically indicates high pressure and stable air moving in, which often leads to fair weather the following day. Conversely, a red sky in the morning can indicate an approaching low-pressure system and the potential for poor weather later in the day.