incongruity

The state of being incongruous, or lacking congruence.

I was told that the Australian Government had had to send my name to London before agreeing to my appointment. My credentials were actually addressed to Her Majesty, despite the fact that the Government of the United Kingdom had recognized the Chinese Communist regime in Peking as early as 1950. No one, however, seemed to notice the incongruity of such an arrangement.

An instance or point of disagreement.

A thing that is incongruous.