'Amr ibnul 'Aas RA reports:
"(Rasulullah SAW gave attention, spoke and showed love to the worst person of a nation. So that, the person may feel he is being given special attention). He used to give attention, and spoke to me also in a manner, that I began to feel that I was the best among the community.
(Therefore one day) I asked:
'O Messenger of Allah, am I better or is Abu Bakr (RA) better?'
He (SAW) replied: 'Abu Bakr (RA)'.
I then asked: 'Am I better, or Umar (RA)?'
He (SAW) replied: 'Umar (RA)'.
I asked: 'Am I better or Uthman (RA)?'
He (SAW) replied: 'Uthman (RA)'.
When I asked him these questions, Rasulullah SAW told me the truth. (He did not tell me I was better to keep me happy. Afterwards I felt ashamed of myself on this deed). I felt I should not have asked such a question".
This Sahabi (i.e. 'Amr ibul 'Aas RA) in the beginning due to the special attention given to him by Rasulullah SAW felt as if he was the best among the community. We find from the first lengthy hadith already mentioned, that it was his (SAW) noble habit to give preference to the best. But, at times, to make one's heart happy and in politeness he gave preference to that which was not the best. He even showed special love to the non-believers and the munafiqeen (hyprocrites).
In the hadith, the order in which the question were asked, is because in the time of Rasulullah SAW the Sahabah RA regarded Abu Bakr RA as the best amongst the people. It is also narrated in the Ahadith that in the time of Rasulullah SAW the Sahabah RA regarded Abu Bakr RA as the best, and after him Umar RA.
Abdullah ibn 'Umar RA relates that in the time of Rasulullah SAW, we did not regard anyone equal to Abu Bakr (RA); after him was Umar (RA), and after him Uthman (RA). After that the other Sahabah (RA) were not given preference. This means that the superiority of these three Sahabah (RA) in this order was manifest. In the time of Rasulullah SAW we the Sahabah (RA) accepted this.
Muhammad, the son of Ali RA, once asked his father Ali RA - who was the best person after Rasulullah SAW?. He replied: 'Abu Bakr RA' I asked after him who? He replied: 'Umar'. There are many other Ahadith wherein during the time of Rasulullah SAW this order is mentioned. Therefore 'Amr RA asked the question in this order. He competed with the one who was regarded as the best, then the second, then the third best. (So the comparison is that) - If I am not better than the first then surely I might be better then the second or the third.