The prophets of old, inspired by the Holy Ghost -
the very same Spirit that Jesus gives His disciples - the very same Spirit that in the NT is called 'the Spirit of Christ' - those prophets routinely and publicly rebuked the people for their sins.
Ezekiel was told by God to eat dung in public, so when people asked him 'what in the world are you doing?' he could tell them 'thus shall God punish you for your sins.'
Isaiah, Jeremiah, etc - they preached publicly and told the people they had sinned, that God was angry at their sinning, and that God would punish them.
This is no different that a preacher today telling the public that God will punish them for their sins, nor is it different that a preacher naming their sins and telling them they are in fact sins against God (and nature - see
Romans 1-2) and that repentance is the recommended course of action.
Telling people that hell awaits them is the truth, if they are not right with God. How shall people be warned, if we fear to offend anyone?
BTW, you cannot truly 'offend' someone by telling them the truth. To 'offend' a person, biblically, means to cause them to stumble and commit sin. It does not mean to upset them.
People got so upset at Jesus' preaching they killed Him.
The servant is not above the Master.