Did Abu Talib die as an infidel due to arrogance, because he rejected Islam by saying: "I would be ashamed to prostrate myself so that my buttocks are higher than my head"?

Abu Talib died upon disbelief, and it is impossible to definitively ascertain the precise reason for his death upon disbelief, whether it was arrogance, bad companionship, or something else. It is narrated in Sahih (definition) al-Bukhari that when Abu Talib was on his deathbed, the Prophet (peace be upon him) entered upon him, and Abu Jahl was present. The Prophet said, "O uncle, say: 'There is no god but Allah,' a word by which I may argue for you before Allah." Abu Jahl and Abdullah ibn Abi Umayyah then said, "O Abu Talib, do you abandon the religion of Abd al-Muttalib?" They continued to speak to him until the last thing he said to them was: "Upon the religion of Abd al-Muttalib." The Prophet (peace be upon him) then said, "I will seek forgiveness for you as long as I am not forbidden to do so." Then the verse was revealed: "{It is not for the Prophet and those who believe to ask forgiveness for the polytheists, even if they were close relatives, after it has become clear to them that they are inhabitants of the Hellfire}" (Quran 9:113). As for what is attributed to Abu Talib in response to the Prophet's call, that he said, "By Allah, you will never subjugate me," this is a very weak hadith (definition).