Why Abu Talib was never converted to Islam?

Answer 1

Allah knows best...according to a hadith in sahih bukhari abu talib did not accept Islam when the prophet asked him on his death bed...

but the shias believe he was Muslim...

i personally belive te sahih bukhari authentic hadith...

Answer 2

He never gave his reason, so we can only guess.

It was not because he feared social rejection or economic hardship. He suffered plenty of this just for protecting Mohammed, so he would not have suffered much worse if he had actually converted to Islam.

It is not stated that he was committed to an alternative religion, such as revering the traditional gods of Mecca. Nor is there any evidence that he disapproved of Mohammed's (or the Muslims') behaviour.

The two best guesses are:

(1) He was not interested in any religion and did not want to commit himself to any of them.

(2) He did not believe Mohammed was a prophet. He did not believe that Islam was true and was not willing to pretend.

Answer 3

For Sunni Muslim's it is believed that he died without accepting Islam.

For Shi'a Muslim's it is believed that he did accept Islam before he passed away.