Ali is the successor of the Rasool Allah. There is mountain load of evidence for it much of which Hazrat Ali present himself. You should study this more. Abu Bakr never claimed or provided solid religious proof for his caliphate. Instead arguments made in his favor were mainly based on old customs and tribal mentality.
Islamic and secular sources both will tell you that Ali did not accept Abu Bakr taking charge. They will also tell you why he refrained from force to claim his rights, including his wife’s who was also wronged by the new ruler.
Bro, read primary books of history and not the re-written glossed over versions. Many of the staunches, the earliest companions, including the tribe of Rasool Allah, Bani Hashim, did not acknowledge Abu Bakr. Please inquire about names and references if you are interested.