All human beings make mistakes, but the mistakes that the Prophet Muhammad (s) were ordained by Allah swt to show that he was not godly, but merely a human like ourselves. The Prophet Muhammad (s) however did not commit a sin, this is one of the reasons why he was chosen to be the last messenger of humankind.
Say: "I am only a human being like yourselves. It is revealed to me that your god is One God. So let him who hopes to meet his Lord act rightly and not associate anyone in the worship of his Lord." (Surat al-Kahf: 110)
One time the Prophet Muhammad (s) was arguing with the cheifs of Makkah, and a blind man came to him with a question. The Prophet (s) was so absorbed in the argument, he didn't hear the man. Allah swt mentioned this in the Quran and told the prophet (s) to correct his mistake. The Prophet (s) then immediately went to see the blind man and apologized. After this, the blind man began to have tears in his eyes. This is because, he felt he never needed an apology, the Prophet (s) was the greatest man, how many times he listened to people no one cared for and answered them, but he only ignored him once, yet he came to apologize right away.
Another story, there was a woman who used to have muscle spasms in her body and mental disease. She bore this disease with great patience and steadfastness. The people asked the Prophet Muhammad (s) about her, he said, she is one of the woman of Paradise.
As can be seen, the Prophet Muhammad (s) was a great man who did not commit sin, yet like everyone else could make mistakes. The example of the Holy Prophet (s) can be clearly demonstrated by the quotes.
"Don't entertain the people with your wealth, but entertain them with smiling face and good conduct."
" He always spoke words that would cause people to love another and come together. He would never frighten or chase them away. He attached great importance to the leaders of all tribes, and was hospitable towards them"
"The Prophet (saas) did not withdraw his hand from another till the latter withdrew his own hand."
Abu Huraira (ra) apparently fainted one day, and the Prophet (saas) lifted him to his feet, took him home, and gave him some milk to drink when he realized he was hungry.
"One cannot be a good believer until he ceases to tell lies, even in jest, and to dispute, even if he is in the right."
"A believer loves for others what he loves for himself."
When the people saw the first fruit (of the season) they brought it to Allah's Apostle (saas). When he received it he said: "O Allah, bless us in our fruits; and bless us in our city; and bless us in our sa's (a measurement unit) and bless us in our mudd (a measurement unit). He would then call to him the youngest child and give him those fruits."
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Peace.
