Why was writing down Hadeeths forbidden for decades despite the fact that the Prophet, sallallaahu ‘alayhi wa sallam, gave ‘Abdullaah ibn ‘Amr ibn Al-‘Aas, may Allaah be pleased with him, permission to write down Hadeeths?
All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
The honorable Companions 
  had different opinions about the permissibility of writing down the Hadeeths of the Prophet, sallallaahu ‘alayhi wa sallam. Some of them, including ‘Umar, Ibn Mas‘ood, Zayd ibn Thaabit, Abu Moosa, Abu Sa‘eed Al-Khudri 
  as well as some of the successors  of the Companions 
  considered the recording or compilation of the Sunnah as disliked. Those who supported this opinion used the Hadeeth narrated on the authority of Abu Sa‘eed Al-Khudri 
  as evidence. In this Hadeeth the Prophet, sallallaahu ‘alayhi wa sallam, forbade the Companions 
  from recording anything about him and commanded that anyone who had written material on his (the Prophet’s) authority other than the Quran, to erase it. [Muslim]
However, other Companions, including ‘Ali ibn Abi Taalib, his son Al-Hasan, Anas and ‘Abdullaah ibn ‘Amr 
  considered it allowable. The supporters of this opinion depended upon several Hadeeths for their view:
- It was narrated on the authority of Abu Hurayrah 
  that the Prophet, sallallaahu ‘alayhi wa sallam, ordered that some Hadeeths be recorded and delivered to Abu Shaat Al-Yamaani 
  as he had asked the Prophet, sallallaahu ‘alayhi wa sallam, for them. [Al-Bukhari and Muslim]
 
- It was narrated that ‘Ali 
  had a sheet of paper on which some rulings narrated from the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, were written. [Al-Bukhari and Muslim]
- It was narrated on the authority of Abu Hurayrah 
  that the Prophet, sallallaahu ‘alayhi wa sallam, gave ‘Abdullaah ibn ‘Amr ibn Al-‘Aas 
  permission to write down Hadeeths. [Al-Bukhari]
- It was narrated on the authority of ‘Abdullaah ibn ‘Amr 
  that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, gave him permission to record all that he said, since he (the Prophet, sallallaahu ‘alayhi wa sallam) said nothing but the truth.
It is possible that the Prophet, sallallaahu ‘alayhi wa sallam, gave those people who were likely to forget his Hadeeths permission to record them. At the same time, he prevented the efficient memorizers from doing this, in fear that they might stop memorizing his Hadeeths and depend solely upon the Hadeeths that they had recorded.  
Another reason is that the Prophet, sallallaahu ‘alayhi wa sallam, may have forbidden writing Hadeeths in fear that they might be confused, if recorded on papers, with the papers on which the Quran was written down, and then later allowed it when this was not likely to occur. 
Later, the disagreement about this issue ended and Muslims agreed upon the necessity of compiling Hadeeths in order to preserve them. 
With regard to the story of writing down Hadeeths, Al-Bayhaqi 
  narrated that the rightly-guided Caliph, ‘Umar ibn Al-Khattaab 
  pondered over the issue and consulted the Companions 
  who agreed with him.  Nevertheless, he continued to make Istikhaarah (the guidance-seeking prayer) for a month, and then preferred that Hadeeths not be written down in fear that people might place too great an importance on them at the expense of the Quran. ‘Umar’s stance affirms what we have mentioned before, that the Prophet, sallallaahu ‘alayhi wa sallam, prohibited the recording of Hadeeths because he feared that some people might confuse it with the Quran. Hence, he prohibited it in general but allowed it in specific cases under certain circumstances. 
Almost all narrations agree that the first person to order the compilation of the Sunnah was the rightly-guided Caliph ‘Umar ibn ‘Abd-Al-‘Azeez 
.  Abu Nu‘aym 
  narrated that ‘Umar ibn ‘Abd-Al-‘Azeez 
  ordered Abu Bakr ibn Hazm 
  who was his appointed governor and judge of Madeenah to write down the Hadeeths of the Prophet, sallallaahu ‘alayhi wa sallam, because he feared that they might be lost. Later, the efforts to compile the Sunnah in book form spread on a large scale and so the books of Sunnah began to emerge.   
Hence, we praise Allaah The Almighty, who preserved His Book (the Quran) and guided righteous men to preserve the Sunnah of His Prophet, sallallaahu ‘alayhi wa sallam. 
Allaah Knows best.
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