According to wikipedia,

A promise is a commitment by someone to do or not do something.

We usually feel obligated to do something once we promise to do it. There is this unspoken rule that we become scum if we do not fulfill the terms of an agreement.
The truth is as tempting as it is to fulfill all promises, we sometimes wonder if we indeed have to fulfill all promises even if they promises.

A critical example is making a promise which endangers countless lives, we have to wonder how it will be like to fulfill such a promise. We have to critically examine the nature of the promise made and ascertain if it is worth fulfilling.

Here is a list of reasons why promises cannot/should not be fulfilled.

If it affects personal integrity
If it threatens people's safety
If it seems too extreme
If it was not made with a sound mind
If it was under duress
In case of emergency

Personal integrity

A promise executed should be a reflection of the person who promised in the first place. A demeaning promise which adds no value to the person who promised and to whom it was promised can be skipped.
For example, promising to run about naked if your favorite team wins a match is not an advisable promise to keep.

Of course, it is a promise nonetheless, but remember that this is a digital age and what ever you do that is captured and uploaded online, stays there forever, this might eventually come back to hunt the person, so why keep to such a promise.

People's safety

Not all promises are safe to fulfill. Any promise which puts anybody in harm's way should not be considered for execution and as such are safe.
Contrary to most people's beliefs, not all promises are debts, a promise which entails reckless endangerment should be laid to rest.

An example of such is a suicide bomber who promises to blow up people, of course when he/she comes to the realization that such is not beneficial and they decide not to fulfill such a promise, they are not supposed to be held accountable because that promise put people in harm's way.

Extremism

I once heard of a story of a guy who died from alcohol overdose because he made a promise and a bet not to stop until he consumes a particular quantity of alcohol.
Guess what, he dies before day break. Now he fulfilled his promise and went to the great beyond and left behind a family to grieve and suffer for what they did not agree to.

Do we excuse the guy for trying to be a man of his words? Of course we do not because he simply did something stupid and his lack of foresight cost him his life and made an innocent lady a widow and some children fatherless.

Not under sound mind

Of course the example I cited in the last point would have sufficed to explain this point, but here is where it differs,the previous point, the man in question was sane when he made the promise and before consuming that much quantity of alcohol, but in this case the person might not even be in the right frame of mind to even make a promise to begin with.

There are instances when people who are hurt will just allow emotions to have the better of them and make promises they never would have in the first place.
A person under stress might do certain things which the person won't do on a normal day, or even display certain traits for example aggression and at the end of the day, the person after calming down might realize the need not to fulfill or execute certain decisions that were taken.

In case of emergency

Some people might wonder how emergencies might cause an individual to break a promise. An example is that of someone who vowed never to have anything to do with a particular and sees that the person has been involved in an accident and requires assistance.
At that point in time, the human nature kicks in, but we have to remember that even rules were made to be broken, how much more promises that need to be broken to save a life.