Because Qunut is supplication, quiet recitation is favored in one Hanafi analysis. Others allow an imam to say it audibly, by analogy with audible recitation. The dispute concerns volume, not the presence of Qunut.
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Quiet or Audible Qunut?
Witr Prayer: Three Rakahs, Qunut and Juristic Differences
Because Qunut is supplication, quiet recitation is favored in one Hanafi analysis. Others allow an imam to say it audibly, by analogy with audible recitation. The dispute concerns volume, not the presence of Qunut.