Assalaamu alaykum wa rahmatullaahi wa barakaatuhu, Shaykh. Did Prophet Ibraaheem (Abraham), peace be upon him, disassociate himself from his disbelieving father while he was alive or after he had died a disbeliever? I read the following:
The father of Ibraaheem was a disbeliever and remained so until he died, and Ibraaheem disavowed himself of him, as Allaah says (what means): {And Ibraaheem’s invoking (of Allaah) for his father’s forgiveness was only because of a promise he [Ibraaheem] had made to him (his father). But when it became clear to him that he [his father] is an enemy of Allaah, he dissociated himself from him...} [Quran 9:114]
Please let me know, Shaykh. Also, please let me know what that disassociation from his father means? Please help me understand. May Allaah reward you.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Prophet Ibraaheem (Abraham) disassociated himself from his father after his death and not during his life because he hoped that his father would become a believer. However, when he died while adhering to disbelief and it became clear to Ibraaheem that his father was among the people of Hellfire, he disassociated himself from him, and he shall do the same on the Day of Judgment.

Ibn Jareer narrated that Ibn ‘Abbaas said, “Ibraaheem kept asking Allah to forgive his father until he (his father) died and, thereupon, he realized that he is an enemy of Allah.”

Mujaahid said about the verse: {But when it became apparent to Abraham that his father was an enemy of Allah, he disassociated himself from him.} [Quran 9:114], “It was when his father died.” Mujaahid also said, “It became apparent to him that his father was an enemy of Allah when he died as a disbeliever.” Qataadah said, “It means that when he died as a disbeliever, he (Ibraaheem) disassociated himself from him.”

As for the meaning of disassociating himself from him in this context, scholars said that disassociation originally means distancing oneself from a matter that causes harm if one is near to it. Scholars mentioned that Ibraaheem disassociated himself from his father in this worldly life by refraining from seeking forgiveness for him and that he will disassociate himself from him in the Hereafter by denying that he is his father when Allah, The Exalted, transforms him into an ugly form. Allah, The Exalted, will ask Ibraaheem, “O My slave, is this is your father?” Ibraaheem will reply, “No, by Your Might, he is not!”

Al-Haafith Ibn Hajar said in Al-Fat-h:

“Scholars held different views regarding the time when Ibraaheem disassociated himself from his father. Some said that it was in the life of this world when his father, Aazar, died as a polytheist (idol worshiper). This opinion was cited by At-Tabari from Habeeb ibn Abi Thaabit, from Sa‘eed ibn Jubayr, from Ibn ‘Abbaas, and its chain of narration is authentic. Another narration says that when his father died, he did not ask forgiveness for him. A similar statement was narrated from ‘Ali ibn Abi Talhah, from Ibn ‘Abbaas, that he asked forgiveness for him during his life, and when he died, he refrained (from asking forgiveness for him)...”

It was also said that he disassociated himself from his father on the Day of Resurrection as he despaired of him when he was transformed, as explicitly stated in the narration by Al-Munthir, as mentioned above. This is also what At-Tabari cited on the authority of ‘Abdul-Malik ibn Abi Sulaymaan:

“I heard Sa‘eed ibn Jubayr say that Ibraaheem will say on the Day of Resurrection, ‘O my Lord, this is my father! O my Lord, this is my father!’

Upon saying it the third time, he will be taken by the hand, and he will turn to him (his father) only to find him transformed into a hyena, so he will disassociate himself from him. It was narrated on the authority of ‘Ubayd ibn ‘Umayr that Ibraaheem will say to his father, ‘I used to command you (to believe in Allah) in the worldly life, and you disobeyed me, and I will not leave you today so hold fast to my waist.’ Aazar will hold fast to his upper arms, but Allah will transform him into a hyena. Upon seeing him as such, Ibraaheem will disassociate himself from him.”

The two opinions can be reconciled by saying that he disassociated himself from his father when he died as a disbeliever and he refrained from asking for forgiveness for him; however, when he saw him on the Day of Resurrection, he felt sorry for him and asked Allah to forgive him. Then, when he saw him transformed, he despaired of him and disassociated himself from him permanently...

Abu Hurayrah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said:

“On the Day of Resurrection, a man will meet his father, whose face will be dark and covered with dust. He will ask his father, ‘O Father, what kind of son was I to you?’ The father will reply, ‘You were a good son.’ The man will say, ‘Will you obey me today?’ His father will reply, ‘Yes.’ The man will say, ‘Hold on to my garment.’ The father will hold on to his garment and he (the man) will go to Allah Almighty as people are standing before Him. Allah will say, ‘O My slave, enter Paradise from any gate you wish.’ The man will say, ‘O my Lord, and my father (will enter) with me. You promised me not to disappoint me.’ Then Allah will transform his father into a hyena, so he will turn away from him. It (the hyena) will fall into Hellfire, and he (the son) will hold his nose (because of the hyena's bad smell). Then Allah, the Almighty, will say, ‘O My slave, is this your father?’ The man will say, ‘No, by Your Might!’” [Al-Haakim graded it saheeh (sound), Ath-Thahabi and Al-Albaani confirmed him]

Allah knows best.