Are you talking about leadership of the Ummah?
You can see it 2 ways:
- Familism leads to leadership.
- Exceptional character and service to Allah, Infallible-ness, divine appointment leads to leadership. It doesn't apply to each and every person of the family though. (This is the reason).
وَإِذِ ابْتَلَىٰ إِبْرَاهِيمَ رَبُّهُ بِكَلِمَاتٍ فَأَتَمَّهُنَّ ۖ قَالَ إِنِّي جَاعِلُكَ لِلنَّاسِ إِمَامًا ۖ قَالَ وَمِن ذُرِّيَّتِي ۖ
قَالَ لَا يَنَالُ عَهْدِي الظَّالِمِينَ
And [mention, O Muhammad], when Abraham was tried by his Lord with commands and he fulfilled them. [ Allah ] said, "Indeed, I will make you a leader for the people." [Abraham] said, "And of my descendants?" [ Allah ] said, "My covenant does not include the wrongdoers."
So Ibrahim asked that others from his children be positioned as Imams. And Allah was like sure. Just not the wrongdoers. In the section below we will see that Allah fulfilled his promise.
The family tree of prophets before prophet Muhammad
As you can see lot of prophets are from the lineage of Prophet Ibrahim (PBUH).
From Ishaq: Jacob, Yunus, Joseph, Job, Moses, Aaron, David, Solomon were all born.
From Ismael: Prophet Muhammad was born
It was actually easier to follow this way, I mean imagine that upon the death of every prophet a new family had to came in to play. God didn't wnat to create more struggle. I mean Moses appointed his brother. Went back to the mountain of Sina, came back and the people had already turned against his brother. A person who's from the family of the predecessor is situated at a more powerful position and people are more accepting!
More specifically about the family of the prophet
إِنَّمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا
Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification. https://quran.com/33/33
In addition because not everyone can become the divine Ummah's leader, there will be more touchstones for who is to be leader. A regular Arab person can't become a leader. In the past centuries many people ( such as Mahdi Sudani, Mirza Ali Muhammad Bab, Qulam Ahmad Qadiani, etc.) claimed to the (false) Mahdi but because none of them had the unique lineage of:
Mahdi Son of Hassan al-Askari, born at the year of 255 Hirji Qamari...none of them were true Mahdis. His lineage makes him unique.
Muhammad was the pride of Arabs and Quraish
قال لقي المنهال بن عمرو علي بن الحسين بن علي ع فقال له كيف أصبحت يا ابن رسول الله قال ويحك أ ما آن لك أن تعلم كيف أصبحت أصبحنا في قومنا مثل بني إسرائيل في آل فرعون يذبحون أبناءنا و يستحيون نساءنا و أصبح خير البرية بعد محمد يلعن على المنابر، و أصبح عدونا يعطى المال و الشرف، و أصبح من يحبنا محقورا منقوصا حقه، و كذلك لم يزل المؤمنون و أصبحت العجم تعرف للعرب حقها بأن محمدا كان منها و أصبحت قريش تفتخر على العرب بأن محمدا كان منها، و أصبحت العرب تعرف لقريش حقها بأن محمدا كان منها و أصبحت العرب تفتخر على العجم بأن محمدا كان منها و أصبحنا أهل البيت لا يعرف لنا حق فهكذا أصبحنا يا منهال
...Minhal ibn Amr met with Ali ibn (AS). Minhal said: Oh (grand)son of the prophet, How did the morning come upon you?
Imam Sajjad: Oh Minhal, shame* on you! If you want to know how the morning came upon me then know:
The morning comes upon us, while we (the family of the prophet among this nation) are like the nation of Israel. "slaughtering our sons and keeping our females alive14:6".
The morning comes upon me, while the best of people after the prophet ( Ali son of Abu-Taleb) have been cursed at the tribunes...Our enemies have been given given wealth and rank...Our lovers have been humiliated and their rights are taken away. This has always been the story of believers.
My days go by while Ajam knows a right for Arabs because Mohammad was from them,
and my days go by while Quraish take pride over Arabs because Muhammad was from them,
and my days go by while Arab knows a right for Quraish because Muhammad was from them,
and my days go by while Arab takes pride over Ajam because Muhammad was from them,
and the days of us the Ahl al-Bayt go by while they know no rights for us, ...that how it is Minhal!
Hadith Thaqalyn from Sahih Muslim: Book 31, Number 5920:
But I am leaving among you two weighty things: the one being the Book of Allah in which there is right guidance and light, so hold fast to the Book of Allah and adhere to it. He exhorted (us) (to hold fast) to the Book of Allah and then said: The second are the members of my household I remind you (of your duties) to the members of my family. He (Husain) said to Zaid: Who are the members of his household? Aren't his wives the members of his family? Thereupon he said: His wives are the members of his family (but here) the members of his family are those for whom acceptance of Zakat is forbidden. And he said: Who are they? Thereupon he said: 'Ali and the offspring of 'Ali, 'Aqil and the offspring of 'Aqil and the offspring of Ja'far and the offspring of 'Abbas. Husain said: These are those for whom the acceptance of Zakat is forbidden. Zaid said: Yes.
Hadith Thaqalyn from Sahih Muslim: Book 31, Number 5923:
Yazid b. Hayyan reported: We went to him (Zaid b. Arqam) and said to him. You have found goodness (for you had the honour) to live in the company of Allah's Messenger (may peace be upon him) and offered prayer behind him, and the rest of the hadith is the same but with this variation of wording that lie said: Behold, for I am leaving amongst you two weighty things, one of which is the Book of Allah, the Exalted and Glorious, and that is the rope of Allah. He who holds it fast would be on right guidance and he who abandons it would be in error, and in this (hadith) these words are also found: We said: Who are amongst the members of the household ? Aren't the wives (of the Holy Prophet) included amongst the members of his house hold? Thereupon he said: No, by Allah, a woman lives with a man (as his wife) for a certain period; he then divorces her and she goes back to her parents and to her people; the members of his household include his ownself and his kith and kin (who are related to him by blood) and for him the acceptance of Zakat is prohibited.
In addition Ismael was son of Ibrahim, Yusuf was son of Jacob, in our daily Tashahud we say اللهم صل علی محمد و آل محمد , there are many verses in Quran speaking nobly of the house of a prophet I mean ال ابراهیم or ال عمران .
أَمْ يَحْسُدُونَ النَّاسَ عَلَىٰ مَا آتَاهُمُ اللَّهُ مِن فَضْلِهِ ۖ فَقَدْ آتَيْنَا آلَ إِبْرَاهِيمَ الْكِتَابَ وَالْحِكْمَةَ وَآتَيْنَاهُم مُّلْكًا عَظِيمًا
Or do they envy people for what Allah has given them of His bounty? But we had already given the family of Abraham the Scripture and wisdom and conferred upon them a great kingdom.https://quran.com/4/54
إِنَّ اللَّهَ اصْطَفَىٰ آدَمَ وَنُوحًا وَآلَ إِبْرَاهِيمَ وَآلَ عِمْرَانَ عَلَى الْعَالَمِينَ
Indeed, Allah chose Adam and Noah and the family of Abraham and the family of 'Imran over the worlds https://quran.com/3/33
the Family of Abraham and Imran have been better families than Adam and Noah
Prophet Muhammad is a descendant from Prophet Abraham.
My point is: historically Arabs, Quriash take pride because Muhammad was from their tribe, nation, but ultimately the Ahl al-Bayt are more deserving of pride. Additionally, the Quran and the narration above is pointing us to the Ahl al-Bayt. Other verses are showing us that the family of Abraham (and therefor the prophet's family) are of the chosen families.
Banu Ummaya was a family dynasty, Banu Abbas was a family Dynasty, why can't Shia also have a family dynasty, with the significant difference that none of the Shia leaders fought to become the ruler—unless the people wanted them. [Ali was the leader so as his duty he defended the Ummah and fought Muawiah, Hassan was the leader but due to his men being bought by Muawiah he made peace with Muawiah. Hussain wasn't the leader, but people wanted him to be, once the people withdrew their support he decided to abort his mission... Yazid didn't want to allow Imam Hussain walk away. He only wanted his life. As a result of Imam Hussain's self defense the battle of Karbala happened. All other Imams didn't do a thing against the rulers of their time because people didn't support them. Instead they were either teaching (Imams Sajjad, Baqir & Sadiq), having intellectual debates (Imam Reza), imprisoned (Imam Kazim) or on house arrest (Imam Hassan al-Askari)]
*Imam used that language as in: Don't you see what's happening/happened to us? How people have forgotten us? It's like someone losing family and then someone asks how was your day!