The concept of possessive individualism is related to the concept of capitalist class. Hobbes belonged to the age of capitalism. Individualism and materialism were the philosophies supporting capitalism.
According to Hobbes, the nature of man is self-centred and materialist. Hence, Hobbesian man is not a social man and not an idealist person. Man is materialist. So, man desires material pleasure. It means man desires property. Hence, the security of life and property are the reasons behind creation of state. Hobbes represented the philosophy of emerging capitalist class. Capitalism in its initial stage required strong state to give protection. Thus, his philosophy is a vindication of the interest of capitalist class of his age.
Possessive individualism means the belief that whatever man owes it emerges out of his hard work and labour. Society has no contribution to it. Hobbes also believes that man is self-centered and self-interested and to man is capable of thinking about another man. So, property of man is the solely the creation of man and society has no role in it.