"Will You Not Be Pleased That You Will Be To Me Like Harun To Musa?"

Sahih al-Bukhari, Volume 5, Book 59, Number 700: 
Narrated Saa'd (ra): 
Allah’s Apostle (saws) set out for Tabuk. appointing ‘Ali (ra) as his deputy (in Medina). ‘Ali (ra) said, “Do you want to leave me with the children and women?” The Prophet (saws) said, “Will you not be pleased that you will be to me like Aaron (Harun) to Moses (Musa)? But there will be no Prophet after me.”
Translated by some like this: (‘Your relation to me shall be like the relation of Harun to Musa…‘) & (‘You hold in relation to me the same position as Harun held in relation to Musa‘)

Hadith in Arabic:

عَنْ مُصْعَبِ بْنِ سَعْدٍ عَنْ أَبِيهِ أَنَّ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ خَرَجَ إِلَى تَبُوكَ وَاسْتَخْلَفَ عَلِيًّا فَقَالَ أَتُخَلِّفُنِي فِي الصِّبْيَانِ وَالنِّسَاءِ قَالَ أَلَا تَرْضَى أَنْ تَكُونَ مِنِّي بِمَنْزِلَةِ هَارُونَ مِنْ مُوسَى إِلَّا أَنَّهُ لَيْسَ نَبِيٌّ بَعْدِي 

There is a wide misconception or misinterpretation about this Hadith by the Shi'ite and even some amongst the Sunni that the first Khalifah was already decided by the Prophet (saws), and that was to be Ali (ra) and not Abu Bakr (ra). However, this Hadith is NOT an evidence of Khilafah of Ali (ra) after the death of the Prophet (saws), because the comparison is with Harun (as), and Harun (as) died before Musa (as) and thus was never his successor after him. 

The following is an explanation by al-Qurtubi in his Tafsir (Tafseer of Ayah 2:30) regarding this narration:

[There is no disagreement that the Prophet (saws) didn’t mean, by (saying) “you will be to me like Harun (Aaron) to Moses” the khilafah after him, and there is no disagreement that Haroon died before Musa… and was not a khalifah after him, for the khalifah (successor of Musa) was Yusha’ bin Noon, so if he wanted by his saying “you will be to me like Harun to Moses” the khilafah, he would have said “you will be to me like Yusha’ was to Musa”, so when he didn’t say this it proved that he didn’t want that meaning, but he wanted that “you are my deputy over my family in my life and my abscence from my family, like Harun was deputy of Musa over his people when he left to speak to his Lord.]

Other Scholars of Ahl As-Sunah explained it the same, him being deputy of the Prophet (saws) over the women and children when he went to the battle of Tabuk just like Musa (as) left Harun (as) as his deputy when he went to his appointment with Allah. 

In a Shi’a site it says:

((To this we answer that whenever the Prophet, peace and blessings be upon him and his family, left the Islamic capital, he would always appoint someone to act as his deputy. If by comparing Ali, peace be upon him, to Harun, the Prophet, peace and blessings be upon him and his family, had intended nothing more than the usual appointment of a deputy, restricted in his authority to Madinah for the period of the Prophet’s absence, why did he not use a similar expression for those other favored Companions he would appoint as deputy? Why did he not use the same or similar words to describe the services they rendered?))

To that we Answer:

Those Sahabah might have not asked the Prophet (saws) to go with him and not stay behind to watch who is left behind from women, children and others, so there was no need for him to tell them that, but Ali (ra) objected to staying behind with children and women and not go to fight with the Prophet (saws), and he wanted to go to the battle instead, so the Prophet (saws) said that to him, showing him that he would be to him, by staying behind watching over women and children, like Harun (as) was to Musa (as) when he left him behind as a deputy over his people, and it is an honor and that he wouldn’t be less than the ones who went to fight in battle.