The most common and most likely answer to this crossword clue is the 12 letter word INCOMPATIBLE
I've seen this crossword clue in The Times
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More clues leading to the result INCOMPATIBLE
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The straight part
We know that "Antagonistic" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case antagonistic = incompatible.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does INCOMPATIBLE mean?
INCOMPATIBLE noun- (chiefly in the plural) An incompatible substance; one of a group of things that cannot be placed or used together because of a change of chemical composition or opposing medicinal qualities.
- A consequent of a contrary.
- Of two things: that cannot coexist; not congruous because of differences
- Incapable of being together without mutual reaction or decomposition, as certain medicines.