When “Abu-Bakr” became caliph, he went on pulpit and said: 

أما بعد أيها الناس فاني قد وليت عليكم ولست بخيركم ... وهذا إسناد صحيح.

O people! I became your caliph while I’m not the best of you…. 

The document of this issue is valid

Al-Bidayah and al-Nahayah, v 7, p6

While Prophet [PBUH] said:

“من تقدم على قوم من المسلمين وهو يرى أن فيهم من هو أفضل منه فقد خان الله ورسوله والمسلمين”

If someone becomes the leader of some Muslims while he knows that there is someone who is superior than him in the society, he’s betrayed god, Prophet and Muslims.

Tamhid al-awae’l, v1, p 481

We ask Sunnis:

1: as “Abu-Bakr” admitted he wasn’t superior than others, so why did he take on the caliphate?

2: according to prophet [PBUH]’s narrative if “Abu-Bakr” is traitor or not?