وَإِذَا قُرِئَ الْقُرْآنُ فَاسْتَمِعُوا لَهُ وَأَنْصِتُوا لَعَلَّكُمْ تُرْحَمُونَ
Meaning: When the Quran is recited, listen attentively and remain silent, so that you may receive mercy (7:204).
The Hanafi argument applies the instruction to listen and remain silent to recitation by the imam in congregational prayer.