So the Doctor of War broke the promise, because he joined the Time War, but why did the 11th Doctor hate him so much for it until Day of the Doctor?
Not only did the War Doctor join the Time War, he finished the Time War by detonating The Moment and wiping out both Daleks and Time Lords.
Or at least that's what he thought, after he regenerated into the Ninth, then Tenth, and Eleventh Doctors. He went for most of his next 3 regenerations actually believing he was guilty of genocide, which broke the promise he made to himself when he chose the name The Doctor.
From The Name of The Doctor Script:
DOCTOR: Look, my name, my real name, that is not the point. The name I chose is the Doctor. The name you choose, it's like, it's like a promise you make. He's the one who broke the promise.
WAR DOCTOR: What I did, I did without choice.
DOCTOR: I know.
WAR DOCTOR: In the name of peace and sanity.
DOCTOR: But not in the name of the Doctor.
From the Day of The Doctor script (I'm writing this from memory, as I've seen it more than 10 times. There could still be mistakes but the message is the same):
CLARA: You told me the name you chose was a promise. What was the promise?
TENTH DOCTOR: Never cruel or cowardly.
WAR DOCTOR: Never give up. Never give in.
Clearly, even though they're the same person, The Eleventh Doctor (and also the Tenth and probably the Ninth) had no choice but to hate the man they were before. We all have regrets, things we wish we could take back, and that was the reason. Only difference is The Doctor being a time traveling alien, actually had the chance to go back and undo his biggest regret.
Because each doctor even though they are the same have quite different personalities and also being a byproduct of regeneration
There are things the thirteenth doctor would never do that the tenth doctor did
There are things the eighth doctor for example did during the time war that led to the actual creation of the war doctor that all the doctors would hate
The ninth and fourth doctors despised the daleks yet the tenth doctor, the twelfth doctor, the seventh doctor, thirteenth and the eleventh would reason with them with during the building of the empire state building Ten asked the daleks to stop and choose peace meanwhile the fourth and the ninth would try to kill them all and of course the ninth because of the time war wanted to kill them even more and the other doctors dont seem to mind too much either way