General Synonyms:
* Contradiction
* Inconsistency
* Dilemma
* Puzzle
* Anomaly
* Irony
* Absurdity
More Specific Synonyms:
* Self-contradiction (emphasizing the internal conflict)
* Catch-22 (referring to a paradoxical situation where options are mutually exclusive)
* Double bind (emphasizing a situation where any choice leads to a negative outcome)
* Oxymoron (referring to a combination of contradictory terms, like "living dead")
The best synonym will depend on the context and the specific meaning you want to convey.