IPA: /ˌɪn.sɪnˈsɪt.ɪ.vɪ.ti/
KK: /ɪnˌsɛn.sɪˈtɪv.ɪ.ti/
The state of not being aware of or not caring about the feelings or needs of others.
His insensitivity to her feelings hurt their friendship.
Insensitivity is formed from "in-" (meaning not) and "sensus" (from Latin, meaning feeling or perception) and "-ivity" (a suffix indicating a state or condition). The word describes a state of not having feelings or being unresponsive to emotional stimuli.
Think of 'not' ('in-') feeling or perceiving ('sensus') — that's why insensitivity means a lack of emotional response.