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If it is a 'Haram' how can the Prophet permit it?

Your companion [Muhammad] has not strayed, nor has he erred, (2)
Nor does he speak from [his own] inclination.(3)
[Quran-53:Surah An-Najm]

All that our Rasoolullah taught us is Allah's commands, not his own desires. In Islam there are exceptions to some rules, many are mentioned in the Quran and many were taught to us through the Prophet's Sunnah, which is mentioned in hadith like the ones mentioned.