The denotation of the word "promise" is "a declaration that one will do or refrain from doing something specified". So, technically speaking, it goes without saying that that's considered binding and therefore "unbreakable". I mean the word actually means unbreakable, so yeah unbreakable as an adjective for promise is redundant.
People do "break their promises" and "change their minds" all the time though. I think that's because people omit that a promise means "no matter what". It doesn't mean "right now" I feel this way. It means "no matter what". It means even when I don't feel the way I feel when I made the promise.
In both examples given (a vow to never drink again, and a vow to be married forever) I also think that social mores have brought about a different connotation. In the 1950's, fewer people walked away from marriage because they saw their vows as binding, as truly for better and for worse. Today society has made it easier to break that vow because it's more important to be "happy". I also think that droves of ppl took vows of abstinence and kept them because a promise is a promise. Today, it's easier to "change your mind" because society tells you that relapsing happens, that you are powerless, or otherwise unable to keep that promise. Never say never, things change, no one knows the future, blahblah...all these are very powerful messages in the world today.
In terms of ending an addiction, I think it's important to know that you will likely feel like drinking after making the promise that you will never drink again. Changing your mind about feeling like drinking is not the same as changing your mind about your promise never to do so.