You have your traffic rules. 
One of them requires you to give way to another where two or more may
interact.  If one does not yield,
suffering of some sort may occur.  Is not
life like this?  How often do you fail to
yield, convinced that you should go first and that your way is the right
way?  Yes, when so many interact, rules
bring order, but in personal exchanges, we recommend carrying around an
internal yield sign for a day and seeing what effect it has.  Let the other go first.  Let the other have their say or their
way.  Do so with no smugness, only the knowing
that in so doing you can find peace.  The
other may remain oblivious to your actions, but you have taken away the
conflict, for it takes two to fight. 
There is only One of you present anyway, and in showing that you need
not always be first or right, you are honoring the Self.  And the last shall be first.