Incongruence is a state of being out of place or incompatible. There would be a certain incongruence to your dad yelling at you and your siblings, "There is absolutely no yelling in this house!"
Use the noun incongruence for things or situations that just don't quite fit or make sense, like the incongruence of one person sliding down a hill on a plastic sled surrounded by skiers and snowboarders. You could also note the incongruence of a grand house that looks perfectly maintained on the outside but is decrepit and rotting on the inside. Incongruence is derived from a Latin word that means "inconsistent" or "not coming together."