It is not a sin to talk during Azaan, As we find no reports of it in the Quran or Sunnah. But It is purely out of respect and obedience that people encourage others to keep silent during the Azaan and to answer the Azaan by repeating after the Muad'in.
But we must be kept quiet and respect the Azaan and we must have to answer the azaan, indeed answering the azaan has great reward.