Worthy of being cherished; deserving to be held dear, loved, or cared for tenderly.
From 'cherish' (Old French 'cherir' meaning to hold dear) plus the suffix '-able' (meaning capable of being). This creates an adjective describing things that merit cherishment.
The word 'cherishable' is rare in modern English, but it perfectly captures what parents feel about their children—not just lovable, but specifically worthy of the active, intentional care that 'cherish' implies!
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