in that passage, jesus basicly says 'dont promise to do (or not do) something - you should be able to say yes or no, and itll be fine. and then he says to strengthen your word with a vow (a promise) shows that something is wrong.
ill just say that two of the things that may be wrong are 1. you say 'i promise' because you dont feel that its enough just to give a simple 'yes' or 'no'
and 2. the person asks you to promise because they arent sure if they can trust you.
in my socializing with kids, both my age and usually younger (kids older than me usually dont have a problem with it - theyve learned that they dont want trust anyone even with a promise), if you say youll do something, they say "promise?" they have been let down so often that they dont know - "can i trust you".
i personally believe that Jesus said this to tell us to trust each other - and to trust yourself that your word will be enough
hope this helps