Usage patterns
無神経な発言をするto make an insensitive remark
He made an insensitive remark about someone's breakup.
〈人〉に無神経なことを言うto say something insensitive to someone
She ended up saying something insensitive to her down-hearted friend.
〈人〉の気持ちを無神経に扱うto treat someone's feelings insensitively
The boss often treats his subordinates' feelings insensitively.