And I'll say it again: if such an oath indeed exists, and Ulfric took it as a prerequisite to beginning his training with the Greybeards, then he was a child when it happened and therefore not able to act freely as an agent of his own will and the oath is null and void anyway. You don't make binding contracts with children. Whether he would've wanted to make such a "contract" as a child is irrelevant. If he was chosen to go to HH and his family sent him there and he had to take some oath or make some vow to make it happen, even if he wanted to do it at the time, ten years later he still has every right to renounce that oath and choose his own path as an advlt. Unless you want to see the Greybeards as the kind of people who choose a child as a student but only on the condition that his entire life will be signed away to them, without the child having the freedom even as an advlt to choose a different life for himself.
And that's still just speculation. Exactly the same you are accusing other people of.
I am responding to the fact that some people keep insisting that Ulfric betrayed the Greybeards by receiving their training and then going out and using it in violation of their philosophy. In order for it to have been a betrayal of that kind, he would've had to have promised NOT to do that prior to being trained.
Ulfric was chosen by the Greybeards when he was a child. That is not speculation, it is confirmed by in-game dialogue. If a lifetime promise to follow the Way had to be made at the time as a prerequisite to his training, then he made that promise when he was a child. Either that, or someone else (for instance, his family) made it for him.
If no commitment to follow the Way was made prior start of his training, then that means that the Greybeards agreed to train him without any promise on his part to adhere to their teachings, and can't complain about a willful betrayal of their trust when the thing they supposedly trusted in never existed.
First of all, I have seen no evidence that any such commitment was either made or required.
Second, people who assume that it was made and then complain that Ulfric broke it are basically complaining that an advlt did not keep a promise made almost ten years earlier, either by himself or others, when he was still a child. That is what boggles my mind, that there are people in the world who think it's reasonable to be pissed off at an advlt for not following through on something he may have agreed to when he was a kid. Really? A kid thinks he wants to be a fireman or a doctor or a monk when he grows up, and then grows up and changes his mind and that's some kind of irredeemable character flaw? That's perfectly normal for a kid. We don't expect them to know, as children, who they are going to be when they reach advlthood or what they are going to want when that day comes. If we're basing our lifetime expectations of them on what they say as children and then get disappointed, that's not a willful betrayal on their part, it's just foolishness on ours.