In context to the Prophet saying Ali was, as Aaron was to Moses, here are some verses from the Bible so we may understand what this means:
Sirach 45: 6: He exalted Aaron, the brother of Moses, a holy man like him, of the tribe of Levi. 7: He made an EVERLASTING covenant with him, and gave him the priesthood of the people …23 Phinehas the son of Eleazar is the third in glory, for he was zealous in the fear of the Lord, and stood fast, when the people turned away, in the ready goodness of his soul, and made atonement for Israel. 24: Therefore a covenant of peace was established with him, that he should be LEADER OF THE SANCTUARY and of his people, that he and his descendants should have the dignity of the PRIESTHOOD FOR EVER.
The LORD said to Moses, 11 "Phinehas son of Eleazar, the son of Aaron, the priest, has turned my anger away from the Israelites; for he was as zealous as I am for my honor among them, so that in my zeal I did not put an end to them. 12 Therefore tell him I am making my covenant of peace with him. 13 He and his descendants will have a covenant of a LASTING PRIESTHOOD, because he was zealous for the honor of his God and made atonement for the Israelites." (Num.25:11-13).
Jeremiah 33:18 The Levitical priests WILL NEVER FAIL to have a descendant in my presence to sacrifice burnt offerings, to burn grain offerings, and to prepare daily sacrifices."
Ezekiel 44:15 "But the Levitical priests, the sons of Zadok, who kept charge of MY SANCTUARY when the sons of Israel went astray from Me, shall come near to Me to minister to Me; and they shall stand before Me to offer Me the fat and the blood," declares the Lord GOD.
As you can see from the above verses Aaron and his descendants (WHO ARE THE ALAY IMRAN) were given the mission as Imams (priests) of keeping purity of the sanctuary (Kabaa) FOREVER. This symbolism parallels Ali sitting on the prophet's shoulders to destroy the idols. This symbolism also parallels the fact that Ali still has his own private door in the Kabaa, which exists to this day. All of it tying in neatly with the Prophet saying Ali is to Muhammad as Aaron was to Moses. (Leading prayer was not a main function of Aaron so hazrat Abu Bakr could have that function without violating the Prophet's promise to Ali).
Now the interesting thing is that both the Jews and the Arabs have abandoned their Imams. However, Islam was created by Allah because the Jews abandoned their Law -the law which required the Jews to obey their Imams. So, we can wonder, has the creator of the world made it so, that both nations will kill each other as the world looks and laughs at them, (zilat in this world) if they fail to follow the Law they were given (obeying the minor tribe he created for them as Imams)? One nation wants to follow Umayyids the other wants to follow tribe of Yahuda, glorifying themselves, at the same time wanting the world to recognize them as spokesmen for God, but neither obeying Allah or glorifying Him. Therefore, both being punished for this hypocrisy. I dont know if this is true, but for an iconoclast it can be something interesting to ponder.
regards,
If you are going to take examples from bible about hereditary succession or leadership you will find plenty. The bible describes Bani Israel as having God that was the God of Israel, the jews were his chosen people, he had different rules for his own people and different rules for people of other tribes.