'challengeable' is formed in English from the noun 'challenge' (from Old French 'chalenge' / 'challenge') + the adjectival suffix '-able' (from Latin '-abilis' via Old French).

The noun 'challenge' entered Middle English from Old French (medieval French) forms such as 'chalenge'/'challenger' and developed in sense from accusations or calls to account to broader senses of disputing or contesting; the suffix '-able' (from Latin '‑abilis') was added in English to form adjectives meaning 'able to be X', producing 'challengeable'.

Originally associated with calling someone to account or accusing (an older sense tied to formal accusation or dispute), the core sense shifted toward 'to dispute or contest' more generally; 'challengeable' thus came to mean 'capable of being disputed or contested'.