Antonyms for the word "Concordable" include words like discordant, conflicting, discrepant, inconsistent, incongruous, and opposing. These words imply a lack of agreement or harmony, and suggest that there is some kind of tension or disagreement between two or more parties. If something is discordant, for example, it does not fit together well with other things, and may create a sense of unease or discomfort. Similarly, if something is opposing, it suggests that there is a fundamental disagreement or opposition between two parties, which may be difficult to reconcile. Overall, these antonyms suggest a lack of unity or agreement, and may imply some kind of conflict or tension.