Answer fool according to his folly or not?

Proverbs 26:1-28
Answer fool according to his folly, or he will be wise in his own eyes. Do not answer a fool accord to his folly, or you will be like him yourself.
Do you see a man wise in his own eyes? There is more hope for a fool than for him.
Like typing a stone in a sling is the giving of honor to a fool.
Like one who seizes a dog by the ears is passer-by who meddles in a quarrel not his own.
Without wood a fire goes out; without gossip a quarrel dies down.
The words of a gossip are like choice morsels; they go down to a man's inmost parts.  morsels: something very appetizing; treat or tidbit.
A malicious man disguises himself with his lips, but in his heart he harbors deceit. Though his speech is charming, do not believe him, for seven abominations fill his heart. Malicious: desire to inflict injury, harm, or suffering on another, either because of a hostile impulse or out of deep-seated meanness卑鄙
His malice may be concealed by deception, but his wickedness will be exposed in the assembly.
If a man digs a pit, he will fall into it; if a man rolls a stone, it will roll back on him. -- Don't do evil trick that could be a snap for yourself.
Why?
These two verse are probably meant to be complementary, not contradictory. It is usually pointless to argue with a fool, but there are times when false reason must be shown up for what it is. 
What could be more nonsensical than fixing a stone to a sling or catapult so that it can't come out?
We are interested in many new things but do not meddle in a quarrel not our own.
How?
Before answer question think about who he is and what this question is?  look into the motivation than answer him.