Impossible to reconcile: irreconcilable differences.
A person, especially a member of a group, who will not compromise, adjust, or submit.
One of two or more conflicting ideas or beliefs that cannot be brought into harmony.
American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.