First off: if you know that you're a sociopath you probably aren't a sociopath.
That being said, your purpose of life is missing a crucial part of the success of a species and that is the ability to not only reproduce but to also bring its young to self-sufficiency. For humans this is a very slow process. Arguably, in a shit world a 6-8 year-old might have the capacity to defend itself to some degree but we are still talking 6-8 years. In the case of species that lack any kind of monogamy and literally exist to live, reproduce, and die their young either mature much faster and/or are produced in such massively high numbers that a few hundred / thousand deaths doesn't dwindle the population. Needless to say, humans simply aren't this way.
Like many mammals, humans have a period of time where both the female and the offspring are vulnerable (while she is pregnant). On top of that, you're looking at years of dedication ensuring that said offspring is taken care of until it is capable of taking care of itself in the modern world. If you were to take your newborn child and toss it out on the street it would die unless someone else came along to take care of it.
Your situation, in which you could care less for monogamy and your girlfriend is not okay with polygamy, is actually a perfect representation of the theory in which men operate differently than women do. As a man we can go around and have sex with as many women as we want and the only consequences we face are those imposed by society. However, each time a woman is impregnated she has to carry the child for 9-months and then take care of it for above-mentioned years. Sure, modern medicine doesn't necessarily make that true but those same theories believe that this knowledge is biologically built into us and even affects our sexual selection.
Anyways, went off into the weeds a bit. The gist of it is: humans aren't like sharks, ants, turtles, alligators, and all these other animals that are prepared to provide for themselves at birth. Reproduction as a human is an investment, and monogamy provides an environment that allows our young to be properly taken care of. Single parenting is a thing, but if you look at it logically it's kind of like putting all the child's eggs in one basket. If that single parent dies the child is an orphan. That's one single parent to influence the upbringing a child.
As for your last bit: if you're confident in your position in her life I don't see why it would be mandatory for you to feel jealous or possessive. You obviously just don't feel like this "ex-friend-with-benefits" is a threat to your position in her life. Not all people are possessive, and not all monogamous relationships end with hurt feelings on both, or even either, side of the relationship. Some people "deal" better than others. And honestly, in most of the modern world you already can do whatever you like with whomever you like as long as there's consent all around. Yet people still frequently pick monogamy.