On the surface these two contradict each other.  However, I am sure the person who compiled this put them next to each other on purpose.  They show us the fine balance that must be maintained in order to be truly wise.  On the one hand, if you answer a foolish argument you might get drawn into foolishness yourself.  On the other hand, if you do not answer a foolish argument you allow others to believe it is wise.  Elsewhere in this passage we have sayings which remind us of the importance of remembering the balance these two show.  Fools will take a wise saying to extremes.

The writer also tells us the importance of words.  Telling lies about people can be as bad and destructive as attacking them.  Rumors and gossip have a way of seeping into our minds and coloring our thoughts.  So, make sure that you know the truth before you say it, and even then think twice if it makes another look bad.  Resist the urge to use something told to you in confidence in order to win an argument.  I hope that those of you reading this can see how these fit together because I thought the words to tie it all together would come to me as I wrote, but they did not.