"Like charcoal to hot embers and wood to fire, so is a contentious man to kindle strife"
This whole chapter is comparing people's actions to natural phenomena so that you can see it more clearly. Solomon is bringing out the causes, cures, and process of foolish behavior. He uses analogies, metaphors, and similes to help us see what is really going on in and with other people. Many times we are just caught up in the actions of others or even in our own reactions to things and do not realize that we can change the outcome of a situation or interaction if we will just understand and act differently.
This particular proverb is a part of a string of proverbs that deals with fire, hatred, and hotheadedness.
Solomon points out that adding fuel to a fire that you want to go out will not work. So adding a contentious person to any situation will usually inflame emotions and enlarge disagreement. There are people who focus their whole life on contentions. They are always ready to see and help others understand how they have been slighted.
Each of the analogies -- charcoal to hot embers and wood to fire -- involves fuel to create a much stronger heat and blaze. Our emotions stirred up against another person are like a fire and adding a contentious person to that mix is sure to add a new level of anger, hatred, irritation, and frustration.
This is the Hebrew word madon, which means strife or contention. There are always two sides in every discussion. There are always other points of view that can be brought up to blunt another person's point of view. There are always points that a person fails to bring up. The contentious person feels the need to bring these up. They push forward the other side. They bring up points that do nothing but inflame others either against them or against others. To contend is to debate and be against.
Notice that Solomon is talking about a contentious person who is not a part of an argument or difficulty being added to it. All of us are tempted, when we are in a disagreement with someone, to want to explain our side to other people. We can choose people who will help us de-escalate the conflict or people who will agree with us or people who will inflame the situation. We know who these people are. "If I tell so and so about this then..." What Solomon is saying to us is do not go to the person who is an expert at contending, the one who enjoys conflict and stirring up anger and disagreement. It feels good to talk to this person because they help you justify your anger against this other person by the extra things they tell you. But they never solve the problem. It feels good, but it only makes the problem worse.
All of us want to feel justified in our position when we are in a disagreement with another person; but if we don't work hard at resolving that disagreement, then we will lose that relationship and all the relationships that grow out of that connection. Realize that every disagreement can grow into a relationship-breaking dispute that carves off a section of people from your life. Small little disagreements can become relationship killers if they are not handled with wisdom, forgiveness, love, and forgetfulness.
When you take your troubles with another person and explain them to an amateur or professional contender, you will have more problems not less. This person will help you feel more outrage and more troubled about the other person. They will twist situations and words in such a way as to make you realize that there is no compromise; there is no way that you could ever trust the other person again.
I have watched couples in marital disputes visit professional contenders who will, for a fee, help you destroy your marriage permanently. They come out of one meeting with the professional contender armed to the teeth with extra charges and new accusations and a new friend in the battle to win the argument. The association with the professional contender never results in strife, anger, and difficulty lessening. It almost always results in divorce, heartache, financial hardship, and relationships being destroyed.
Be careful who you invite to "help" you with your arguments and disputes. Unless you are permanently willing to dissolve relationships and carve out a section of people from your life forever, don't bring in a contentious person as a consultant or counselor. They will add wood to the fire of your rage.
Let me add that that there is a place for a professional contender for the helpless or to be the advocate for a person who has been immorally or unjustly treated, but bringing your situation to a professional contender still fractures the relationship and enflames the situation.
Solomon's advice is don't invite a contentious person into your disputes. Understand what different people will do to the relationships and situations of your life. It is not that difficult to grasp what the end result will be of explaining your situation to the different people in your life. Think it through before you explain to the different people in your life what you are going through. Some of the people you know should not hear the whole story. They may make you feel good, but they will not really help you or the situation.