Well the basic "rational" argument for polyamory is very similar to the standard "rational" argument for communism from a century ago.

Argument for communism:

Why do we insist on treating objects and land like they have some metaphysical and exclusive "belongs to so-ans-so" property? Such metaphysical properties don't have any connection to reality and they cause lots of suffering and restrict people's freedom. And, oh yes, look at this successful collective-propery community. [Conveniently ignore all the collective-property communities that failed or blew up.]

Argument for polyamory:

Why do we insist on treating people like they have some metaphysical and exclusive "married to so-and-so" or "so-and-so's SO" property? Such metaphysical properties don't have any connection to reality and they cause lots of suffering and restrict people's freedom. And, oh yes, look at this successful polyamorous community. [Conveniently ignore all the polyamorous communities that failed or blew up.]