Parents really exploit, if not abuse, the power of promise with their children as a form of coercion, sometimes (unpleasantly) appended with 'cross your heart and hope to die' or 'on your father's grave' and so on. (By the way, no prizes for guessing the origin of those phrases.) Children, in turn, pick up on this versatile linguistic pattern and use it to devastatingly manipulative effect themselves.
The reason it's such a potent weapon is that an explicit continued commitment to something is such an important way for us to demonstrate our sanity to the world. That's why politicians are constantly accusing each other of 'flip-flopping' or 'doing u-turns', as if changing your mind was A Bad Thing; and it's why we find it so hard to alter our acquired beliefs and behaviours. A consistent belief in anything is perceived better than one that is always switching.
In adulthood, although promise seems on the face of it a pretty harmless word, in actual fact, owing to its very strong subtext, we rarely or reluctantly use it - test that out by asking for some promises.
And that's why I like it so much - it's a word that can touch a person intimately, it really means something, really affects on a deep emotional and behavioural level. So, rather than 'will you?' or 'I will...', it's 'do you promise?' and 'I promise...'. Feel the difference.