Brearley, writing in his column for 'The Times', said Anderson is not being a role model when he crosses the line of proper respect.
"Earlier in the summer, when the kerfuffle with Ravindra Jadeja was first publicised, an England spokesman said the management back their key bowler to the hilt," Brearley said.
"I would agree about competitiveness - a top sportsman needs it (to the hilt). Such an attitude is a form of respect to the opposition. ," he said.
"By all means encourage Anderson (and others) to be aggressive; but surely one can, at the same time, confront the boorishness of some of his gestures and language," he said.
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The infamous pushgate incident took place as the players were leaving for lunch during the second day of the first Test at Trent Bridge.
But the ICC's judicial commission has pronounced Anderson not-guilty, and later the international body also rejected BCCI's review plea of the verdict.
"So by all means encourage Anderson to harness his aggression, to give full rein to his terrific skill, to honour his own truth, to avoid timidity or 'nicey-niceness'. But not at the expense of respect and humour," he said.