Patriarchy and sexual monogamy are co-morbid - they both arose at the same time. We see even today in cultures where the whole community shares food and takes care of each other than paternity is not that big a concern. The Standard Narrative of evolution that men do not want to work to raise other men's genetic offspring is a very recent development. Before patriarchy (10K years ago) it wasn't an issue and still isn't in some contemporary cultures.
“A female who mates with several different males will have more genetically diverse offspring, boosting the chances that at least some of them will thrive.” Source This goes for human females as well as other non-human animals and it is confirmed in our anatomy. The coronal ridge of the human penis is specifically designed to displace semen left there by another man or men. In addition, animals that engage in mate competition prior to copulation (like gorillas) tend to have small testes and penises. Animals that instead engage in sperm competition are more well endowed relative to body size (like chimpanzees and humans) because they need to have a large supply of semen on hand to inseminate multiple partners.
Partible paternity, where several men have sex with a woman and are considered the father of her child is a long-standing practice in some parts of the world and a far from rare dynamic even today. Spreading fatherly feelings throughout the group helps to maintain solidarity and cohesion as well as promotes the well-being of a greater number of children.
As you have pointed out, jealousy (which is based in insecurity and the desire to control) is a patriarchal impulse, and since anthropologists agree that social dynamic only arose with the advent of agriculture less than 10K years ago, it's a very new development. In a culture where everyone looks out for each other and the good of the tribe/community, there is a whole lot less jealousy and controlling behavior.
(With patriachy/agriculture)" Labor roles became more gendered as well. Generally, men did the majority of the fieldworkwhile women were relegated to child-rearing and household work. Without contributing food (and by association, without control over it), women became second-class citizens. Women also had babies more frequently, on average once every two years rather than once every four in hunter-gatherer societies.
Because somebody had to have control over surplus food, it became necessary to divide society into roles that supported this hierarchy. The roles of an administrator, a servant, a priest, and a soldier were invented. The soldier was especially important because agriculture was so unsustainable compared to hunting and gathering. The fickleness of agriculture ironically encouraged more migration into neighboring lands in search of more resources and warfare with neighboring groups. Capturing slaves was also important since farming was hard work, and more people were working in these new roles."
