A hadeeth was narrated by al-Bukhary, that the Mother of the Believers, Sawda Bint Zam'a, made a deal with the prophet Muhammad PBUH, by which she waived her day to the Mother of the believers, Aisha, after he PBUH decided to divorce her because she became old. This event was considered a reason for the verse (4:128: And if a woman has reason to fear ill-treatment from her husband, or that he might turn away from her, it shall not be wrong for the two to set things peacefully to rights between themselves: for peace is best) and more, this was considered an Islamic solution to prevent divorce (that the woman should give up some of her rights ) I don't agree on this, because from my understanding of the verse we see that it says if a woman fears that her husband may leave her they should both make a deal and try to figure out a solution, not as was told by Mufassereen, that only the woman should give up her rights. Also, how can the solution of this fear of being left by her husband, be a deal in which her husband leaves her? And I also wonder how the word divorce was figured out in the Tafseer of this verse while the Quran didn't mention it, and when the Quran is referring to divorce it says it explicitly?
From what we know from the same book (Bukhary) and the other books of (Sunan & Sahih), the Prophet PBUH, married her for a noble reason, which was that she was a widow and had orphan children, and she was an old lady when he decided to marry her, and that’s why she refused at the beginning (saying that she is an old woman with five children and no one would like to marry her), so if we agree that the prophet wanted to divorce her because she was old, that cancels the noble aim of the Prophet’s marriage, as this contradicts the fact that the prophet married her while she was old, and also the reason of the verse is contradicting with its meaning. Would you please help me in understand this and clear my doubts?

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 ‘alayhi wa sallam, is His slave and Messenger.

Our answer to the misunderstanding that you mentioned in the question is as follows:

It was not Sawdah whom the Prophet married while she was advanced in age and had children; rather, that was Umm Salamah .

Al-Bukhari did not mention that Sawdah granted her day to ‘Aa’ishah because the Prophet decided to divorce her. Rather, it was stated that "she did so wishing to please the Prophet ." Moreover, Abu Daawood reported, "when she was advanced in age and she feared that he would separate from her…", so it was she who feared that he would separate from her, but it was not stated that it was the Prophet who decided to separate from her.

Furthermore, it was mentioned in another narration that she said, "I do not have any need for men”, but there was no authentic narration which stated that the Prophet informed her that he, sallallaahu ‘alayhi wa sallam, wanted to divorce her, or that he, sallallaahu ‘alayhi wa sallam, divorced her. Therefore, it becomes clear that it was just fears from Sawdah when she felt that she was advanced in age and that it was difficult for the Prophet to stay overnight with her (in the same manner he stayed with each wife), so she took the initiative for this. But he did not initiate divorce against her and he did not tell her that he wanted to divorce her.

Al-Bukhari did not state that the reason why the verse was revealed is about the story of Sawdah but he stated that ‘Aa’ishah narrated, “A man would have a wife and he does not have any need for her and he wants to separate from her, and she would say, ‘I forfeit my right on you’, and then this verse was revealed about this matter.” In another narration, also reported by Al-Bukhari ‘Aa’ishah narrated, "A man would see in his wife what he does not like, either her advanced age or else, and he would wish to separate from her, and she would say, ‘Keep me and give me my share of spending the night with me according to your wish’”, and she (‘Aa’ishah) said, “It is alright if they agree.”

However, Abu Daawood narrated in his Sunan that ‘Aa’ishah mentioned something which suggests that the verse was revealed about the story of Sawdah but it was also reported that the verse was revealed in general. Moreover, it was reported that the verse was revealed about the story of the wife of Raafi’ ibn Khadeej when he wanted to divorce her. Therefore, it cannot be authoritatively asserted that the verse was specifically revealed about the issue of Sawdah ; rather, it was revealed to solve the issue in general, and so, it included the issues like the one of Sawdah and the wife of Raafi’ ibn Khadeej and others.

The Prophet was a human being like us; Allaah The Almighty Says (what means): {Say, “I am only a man like you to whom has been revealed that your god is one God.}[Quran 18:110] He liked and disliked certain things and he got displeased as well. So, he, sallallaahu ‘alayhi wa sallam, is not to be blamed if he, sallallaahu ‘alayhi wa sallam, was not attracted to one of his wives and wanted to divorce her, and then she reconciled with him by renouncing some of her rights so that she would get the honor of staying with him as his wife.

This verse included a just and merciful ruling, and a correct guidance from our Lord, which is that if a wife expects contempt (cruelty) or desertion on her husband’s part because of her advanced age or because she is not beautiful, and her husband marries another wife, then she may reconcile with him in a way to remain in her home honored and dignified, and she would forfeit some of her rights on her husband – such as his sharing her bed – and renounce some of the obligations that her husband is obliged to fulfill towards her; this is better for her than divorce.

Allaah Knows best.