Comparative form of finicky; more fussy, picky, or hard to please than something else.
From finicky (adjective) plus -er suffix forming the comparative degree. Finicky itself derives from finick, showing how English converts verbs and nouns into adjectives and then creates comparatives.
The word 'finickier' proves English speakers have been complaining about picky eaters for centuries—children haven't changed, but the vocabulary we use to describe their behavior has evolved dramatically!
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