Is boycotting a 15-year-old brother because of his denunciation of the prohibition of watching forbidden things and his not lowering his gaze correct, or is there a more appropriate reaction?

You must continue to advise the disobedient brother with gentleness and kindness, reminding him of the virtue of patience in refraining from sin. It is not advisable to abandon him unless there is an overriding benefit in doing so that might deter him. You must be patient with him and not let anger lead you to transgress the limits set by Allah, as happened in the story of the worshipper whose deeds were nullified due to his haste in judging his sinning brother.