IPA: /ˌʌn.rɪˈkɒn.sɪl.ə.bəl/
KK: /ʌnˌrɛkənˈsaɪləbəl/
Describing two or more things that cannot be made compatible or brought to agreement.
The two sides had unreconcilable differences that made negotiation impossible.
Unreconcilable → It is formed from "un-" (meaning not), "re-" (meaning again), and "conciliare" (meaning to bring together or reconcile). The word describes a state of being unable to be brought together or reconciled again.
Think of 'not' ('un-') being able to 'bring together' ('conciliare') again — that's why unreconcilable means something that cannot be reconciled.