irreconcilable

adjective2

1. •
   Unable to be reconciled; opposed; uncompromising.
2. •
   Incompatible, discrepant, contradictory.

   • I amused myself by thinking that in his choice of books he showed pleasantly the irreconcilable sides of his fantastic nature. — 1919

noun1

1. •
   Something that cannot be reconciled.

noun2

1. •
   (slang, old-fashioned) A Confederate who moved to another country following the American Civil War, rather than live in a reunited United States.
2. •
   (slang, old-fashioned) A vociferous opponent of the Treaty of Versailles.