In order to truly understand the logic behind Hobbes's claim, we must first understand his point of view of human nature. The key element in Hobbes's view on human nature was the importance of desires. Unlike many other philosophers such as Plato and Aristotle, Hobbes had a different approach to desires. He believed desires were real motive behind human behaviors. (Leviathan, p119) What motivated human actions were not virtues such as wisdom as Aristotle and Plato would claim, nor was it a sense of duty as Cicero would say. It was rather simple desire. Hobbes did not see desire as a harmful feeling, which must be avoided. He rather thought of it as a positive part of human nature, which could drive a person to achieve more and more.
Hobbes had a definition of happiness closely connected to desires. Hobbes defined happiness as a "continual successe in obtaining those things which a man from time to time desireth" He used the phrase "felicity" for this definition of happiness. (Leviathan, p.129) Important point here is, there is no limit to this attaining of goods and happiness is a continued process of desire fulfillment, which lasts from birth to death.
It would not be wrong if we claim all reasonable people would like to live a life of happiness or in other words, a life of felicity. Having accepted Hobbes's definition of felicity, it can be further said that all people would want a life where all their desires are fulfilled.
Hobbes argued that despite minor differences, all people were close to being the same in both ability and intelligence. (Leviathan, p.183) Hobbes further stated, because people are close to being the same they...