People get into nonmonogamous relationships because they a) want to be in a relationship and b) don't buy into the traditional narratives of what relationships need to look like (i.e. monogamy). This is, I think, actually pretty reasonable! There are all sorts of reasons to question normative relationship scripts, and it's not inconceivable that some people who question whether or not these narratives are right for them might eventually decide that no, they don't think they are.
So polyamory comes from people looking at 'a man and a woman date, then eventually marry and have children' and responding that they think it's unnecessarily restrictive. And it is! The queer movement has fairly successfully pointed out that it's possible to contravene this diktat and live a happy, fulfilled life. And so we get, I think, a polyamory (as distinct from the general case of nonmonogamy) which is inherently antihegemonic, in design if not always in practice. The poly people I know tend to stress that 'open relationship' and 'nonmonogamous relationship' often function differently - a poly relationship is a relationship like any other, but potentially one with more people in it.
Knowing whether or not any particular relationship structure would work for you (or your sister, or your father) isn't the same as knowing if a particular relationship structure is equitable and just. And there's no specific reason, besides jealousy, that polyamory should necessarily be inequitable or unjust. Poly relationships seem to fail for the same reasons that monogamous ones do (albeit writ larger), and the people who claim they work for them tend to either say that jealousy isn't really a concern or that they have mechanisms (regular processing sessions is one I've seen a few times) to address potential jealousy before it can become an issue. Sometimes (often?) this all crashes and burns because people went 'aha, I don't need the master narrative!' but forgot to learn how to actually be in a relationship along the way.
(also you get to have sex with someone other than your partner without it necessarily causing trouble, so i'm sure that's a draw too)