Biology and Division of Labor

In the first two paragraphs of the 'Private Property and Communism' section of the German Ideology, Marx-Engels assert: 1. The traditional nuclear family is the foundational instance of "natural" Private Property; 2. Private Property and Division of Labor are equivalent; and 3. Natural Division of Labor is abolished in Communism. Hence, though not explicitly articulated in the passage, the division of labor in the traditional nuclear family is abolished in Communism, perhaps e. g. replaced by a more egaltarian father-mother relation, by communal child-raising, etc. However, they seem to not recognize that an implicit relation undermines the entire sequence. For, the fundamental division of labor in any family is that which originates it--source of sperm and source of egg. So, since there is no natural property relation entailed in that division of labor, #2 is false, and since it remains unaltered by Communism, #3 is false, as well. More generally, the sequence reinforces what was previously proposed--that the larger context of Socialism is Biological, i. e. that it is conditioned by some Vitalist principle.