Synonyms for Unaccountable (same or very similar meaning)
WordNet sense 1 (showing lack of care for consequences):
irresponsible
WordNet sense 2 (not to be accounted for or explained):
unexplainable
WordNet sense 3 (incapable of being explained or accounted for):
incomprehensible, inexplicable
From the ODE community, based on WordNet
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