To take offence is to feel insulted by what was said. The room goes quiet and somebody's jaw has gone tight.
The grammar is worth noticing: the insulted person takes it and the speaker gives it, so the thing passes between two people like an object. It takes at — he took offence at the word amateur. No offence and none taken are the fixed exchange that heads it off, easily offended is what you call somebody who does this often, and Americans spell the noun offense.
1phrasetake offenceTo feel insulted by what was said.
“He will take offence at almost anything.”
take offence is a reaction of hurt pride.
Also accepted in games: take offense
Practised in Common Word Pairs