'dismissibility' comes from the verb 'dismiss' + the nominalizing/adjectival suffix '-ibility' (from Latin '-ibilis'), where 'dismiss' itself derives ultimately from Latin 'dimittere' ('di-'/ 'dis-' + 'mittere' meaning 'to send away').

'dismiss' entered English via Old French and Middle English from Latin 'dimittere'; the suffix '-ibility' entered English via Late Latin '-ibilis' and French formations, producing 'dismissibility' as a modern English noun built from these elements.

Originally the root meant 'to send away' (Latin 'dimittere'); over time the sense broadened to include 'to remove from office or reject', and 'dismissibility' came to mean the capacity to be dismissed or rejected.