From the words of a hadith, it seems that Amir Muawiya (may Allah be pleased with him) considered himself more deserving of the caliphate than Sayyiduna Hasan bin Ali (may Allah be pleased with him) and his father Sayyiduna Ali bin Abi Talib (may Allah be pleased with him), or Abdullah bin Umar (may Allah be pleased with him) and his father Sayyiduna Umar (may Allah be pleased with him).
First of all, please observe the complete hadith and its translation:
عَنِ ابْنِ عُمَرَ، قَالَ: ” دَخَلْتُ عَلَى حَفْصَةَ وَنَسْوَاتُهَا تَنْطُفُ، قُلْتُ: قَدْ كَانَ مِنْ أَمْرِ النَّاسِ مَا تَرَيْنَ، فَلَمْ يُجْعَلْ لِي مِنَ الأَمْرِ شَيْءٌ، فَقَالَتْ: الحَقْ فَإِنَّهُمْ يَنْتَظِرُونَكَ، وَأَخْشَى أَنْ يَكُونَ فِي احْتِبَاسِكَ عَنْهُمْ فُرْقَةٌ، فَلَمْ تَدَعْهُ حَتَّى ذَهَبَ، فَلَمَّا تَفَرَّقَ النَّاسُ خَطَبَ مُعَاوِيَةُ قَالَ: مَنْ كَانَ يُرِيدُ أَنْ يَتَكَلَّمَ فِي هَذَا الأَمْرِ فَلْيُطْلِعْ لَنَا قَرْنَهُ، فَلَنَحْنُ أَحَقُّ بِهِ مِنْهُ وَمِنْ أَبِيهِ، قَالَ حَبِيبُ بْنُ مَسْلَمَةَ: فَهَلَّا أَجَبْتَهُ؟ قَالَ عَبْدُ اللَّهِ: فَحَلَلْتُ حُبْوَتِي، وَهَمَمْتُ أَنْ أَقُولَ: أَحَقُّ بِهَذَا الأَمْرِ مِنْكَ مَنْ قَاتَلَكَ وَأَبَاكَ عَلَى الإِسْلاَمِ، فَخَشِيتُ أَنْ أَقُولَ كَلِمَةً تُفَرِّقُ بَيْنَ الجَمْعِ، وَتَسْفِكُ الدَّمَ، وَيُحْمَلُ عَنِّي غَيْرُ ذَلِكَ، فَذَكَرْتُ مَا أَعَدَّ اللَّهُ فِي الجِنَانِ، قَالَ حَبِيبٌ: حُفِظْتَ وَعُصِمْتَ
Reference: (Sahih Bukhari:4108)
Translation: Abdullah bin Umar رضي الله عنهما narrated that I went to Hafsa رضي الله عنها and water droplets were dripping from her hair. I said to her, "You are witnessing the people's matter, and nothing has been reserved for me in this matter." Hafsa رضي الله عنها said, "Go to the gathering of Muslims; people are waiting for you. It may happen that your absence at the moment causes further division." Finally, upon Hafsa رضي الله عنها's insistence, Abdullah رضي الله عنه went. Then, when the people left, Muawiyah رضي الله عنه gave a sermon and said, "Whoever wants to speak on this matter, at least raise your head. Surely, we have more right in this matter than him and his father." Habib bin Muslimah رضي الله عنه said to Ibn Umar رضي الله عنهما about this, "Why did you not respond to him right there?" Abdullah bin Umar رضي الله عنهما said, "At that moment, I gathered my clothes (ready to respond) and intended to say that the one who has more right in this matter than you is the one who fought for Islam against you and your father. But then I feared that my words might increase discord among the Muslims and lead to bloodshed, and that my words might be misunderstood against my intention. Instead, I remembered the blessings of Paradise that Allah has prepared in Paradise for the patient." Habib Ibn Abi Muslim said, "It is good that you remained safe and were saved, and did not fall into calamity."
First Point
In light of the aforementioned hadith, the first point is that the words of Sayyiduna Abdullah bin Umar: ’’ فَلَمْ يُجْعَلْ لِي مِنَ الأَمْرِ شَيْءٌ‘‘ Translation: Nothing has been reserved for me in this matter, there is no complaint about not receiving the governance because there is no clear evidence that the word " الامر” means governance. And even if it is assumed that it does mean governance, then it is not an expression of complaint but rather an explanation of the reason for not participating in that gathering.
Second Point
It is established that Sayyiduna Umar bin Al-Khattab (may Allah be pleased with him) also did not consider the caliphate suitable for his son Abdullah bin Umar, to the extent that when people expressed their allegiance to Abdullah bin Umar, he forbade them from doing so.
Reference: (Tabaqat Ibn Saad: 4/151)
Here it should also be understood which gathering the conversation between Sayyiduna Abdullah bin Umar and Sayyida Hafsa is about? Allama Haithami considered it an incident during the truce of Sayyiduna Hasan bin Ali, but the commentator of Bukhari, Hafiz Ibn Hajar, may Allah have mercy on him, refuted this.
Reference: (See: Majma' al-Zawa'id: 4/242, Fath al-Bari: 7/403)
Ibn al-Jawzi considered it the gathering at the time of the pledge of allegiance to Yazid bin Muawiya, but Hafiz Ibn Hajar also refuted this opinion, and in his own view, it was the gathering at the time of Tahkim during the Battle of Siffin. See:
Reference: (Fath al-Bari 7/403)
Third Point
Did Amir Muawiya, may Allah be pleased with him, consider himself more qualified than Umar Farooq, may Allah be pleased with him, as some people have inferred from the words of the narration ’’ فَلَنَحْنُ أَحَقُّ بِهِ مِنْهُ وَمِنْ أَبِيهِ ‘‘?
In fact, if no name is mentioned in the narration, it should be understood that Amir Muawiyah رضي الله عنه spoke generally without specifying anyone, because firstly, Amir Muawiyah رضي الله عنه's words are general, and secondly, there was no disagreement between Hassan bin Ali or Abdullah bin Umar رضي الله عنهما and Amir Muawiyah رضي الله عنه, so why would Amir Muawiyah رضي الله عنه mean them?
In the narration of Musannif Abdul Razzaq, a narrator has said that it refers to Abdullah bin Umar, but this is the statement of a narrator, not of Abdullah bin Umar himself, and since it is the statement of a narrator, it could also be mistaken. See:
Reference: (Musannif Abdul Razzaq 10530)
.Also, the mention of the father along with the son is not in the literal sense; rather, Arabs often use this style of mentioning the father as an exaggeration in their speech.
The summary of the discussion is that in a general manner, without referring to any specific person, Sayyiduna Amir Muawiya رضي الله عنه said these words and by saying "منه ومن أبيه” meaning "from him and his father," he further strengthened the point.
Fourth Point
"الامر” does not mean the caliphate but rather the revenge for the blood of Sayyiduna Uthman. In this matter, Sayyiduna Amir Muawiya considered himself the most entitled. In fact, many scholars also hold this view. For example, Allama Aini says:
فإنه ولي عثمان بن عفان والمطالب بدمه وهو أحق الناس
Translation: He (Amir Muawiya) was the guardian of Uthman ibn Affan and sought revenge from his killers and was the most entitled among the people for this.
Fifth Point
It cannot be taken to mean the caliphate also because Sayyiduna Amir Muawiya himself considered Ali ibn Abi Talib رضي الله عنه superior to himself and more deserving in matters of the caliphate.
Reference: (Seer A'lam al-Nubala:3/140)
Sixth Point
From the words of Sayyiduna Amir Muawiya, it is certain that Sayyiduna Umar and Abdullah ibn Umar cannot be meant, as Hafiz Ibn Hajar said:
وقيل: أراد عمر وعرض بابنه عبد الله، وفيه بعدٌ؛ لأن معاوية كان يبالغ في تعظيم عمر
Reference: ( فتح الباری:7/404 )
Translation: It has been said that Sayyiduna Amir Muawiyah meant Umar and Abdullah bin Umar, but this is impossible because Sayyiduna Muawiyah used to hold Sayyiduna Umar in very high esteem.
