The Fatal Flaw of the Common Ownership of the Means of Production

I reason that there is a contradiction of "anarchists" who advocate for the "common ownership" of the "means of production.

The "means of production" being the means by which products are produced; "common ownership" being ownership in common of all individuals of a given material by which products are produced.

For, is not the human-body and its attendant labors, also a "means of production"?  Indeed, I think that one advocating the "common ownership of the means of production" does so advocate because of the premise that the laborers upon the "means of production" have greater claim to the product of the "means of production" than the "capitalist" or "illegitimate owner of the means of production".

If the human-body is indeed, the (primary) "means of production" then therefore, given the assertion that the means-of-production must be commonly 'owned', each human-body must be considered to be held in "common ownership" [of course, this would also have the interesting implication that every laborer, is a capitalist, as the 'owner' of the "means of production"].

Generally, when one person, does not own themselves, but it owned by another person, or conglomeration of persons, this state or condition, is commonly referred to as a condition of slavery.

Which is to say, that those who advocate the "common ownership" of the "means of production" are advocating a theory in which no person owns themselves, but is owned in common with all others, and that same individual, in her turn, has common ownership of all other persons.

This theory then, implies a condition of perfect slavery of all individual persons; and one might think that this proposition of universal slavery of all persons is not appropriate to anyone claiming the denomination of "anarchist", for that denomination would only be a rebellion of domination that implies the enslavement of all.