IPA: /ɪnˈsɛnsəblnəs/
KK: /ɪnˈsɛnsəblnəs/
The quality of being unable to feel or respond to sensations or emotions; a lack of awareness or sensitivity.
His insensibleness to the suffering of others was shocking.
Insensibleness is formed from "in-" (meaning not) and "sensibilis" (from Latin, meaning able to be perceived or felt) and the suffix "-ness" (meaning the state of being). The word describes the state of being unable to perceive or feel, hence lacking sensitivity.
Think of 'not' ('in-') being able to 'feel' ('sensibilis') — that's why insensibleness means the state of not being able to feel.