1.) Hobbes has both a philosophy of the person and of political relations. They are tightly connected and cross-justify each other, but if you only have time to learn one, learn the political philosophy, the success of which is much easier to see and much harder to contest.
2.) Human Equality. For us, human equality is a great point of pride and source of dignity. If all are equal, so we think, we can all be friends and no one has a right to exploit or subjugate anyone. Hobbes agrees with our vision of equality but sees it as much more problematic than we do.
Equality is the absence of greater and lesser, or of natural hierarchies. Bees and termites have natural hierarchies and so are not born equal. Human beings have nothing like this: some are born drones, others workers, others the queen. But government consists in hierarchy, and so human persons by nature have no government. We might have families and even small tribes with recognizable hierarchies, but nothing much beyond this.
3.) The State of War. The absence of hierarchy or rule gives everyone by nature the powers that a king has during war. While there are some limits even here, they are so broad and expansive as to be basically infinite. Kings in time of war do things that, for a citizen in a time of peace, would be called murder, fraud, kidnapping, unjust imprisonment. Notice the problem of what we usually take to be so ennobling and dignifying about free democracy: “Every man a king”.
4.) SPNBH. Every man a king, however, leaves us with an obvious lack of social stability. Contracts need not be honored, long-term planning and co-operation becomes largely a wasted effort, and no one can count on the sort of social mechanisms that are indispensable to have utilities, trade, stable institutions like universities, stores, road-building crews, engineering… In other words, anything recognizably social, ennobling, and beneficial to life disappears. By nature, in Hobbes’s lapidary conclusion, human life is solitary, poor, nasty, brutish. and short.
5.) The Solution. the political solution consists in man abandoning natural right or in having it taken from him. It is renounced birthright, and so a solution that is inherently unstable and even what a scholastic would call violent, i.e. contrary to a natural impulse.