As a colossal sucker for storybook romance, polyamory or anything related to it is pretty much my catalyst for rampant screeching.
It's just so utterly alien an idea, and it's clearly just an attempt to pretty-up wanting to bang more people under the guise of being 'empowered romantically' or whatever. These people have probably never felt actual love in their lives - which isn't the initial attraction, but the force that makes two people stay together (which sounds like something from a cheap romcom, but it's what I've been told by most old married couples I've spoken to).
In the end I don't really have much of an argument against it other than 'it's stupid', but it's a very loud argument I will scream at people until the end of time.