Let's consider offspring. There's no method of contraception 100% effective at preventing pregnancy. Even if all available methods are combined and each is used correctly, the risk is still nonzero. Sooner or later it will happen. Once it does, there's a life-or-death choice to be made, together with all the financial, social, legal, emotional, and other baggage associated with it.

Entanglement happens other ways too. Physical intimacy is tightly bound to emotional intimacy. It's how we all are wired, and that's a Good Thing^TM. Without that bond, sex would be reduced to a mere mechanical act: hollow and unsatisfying. But with that bond comes a truckload of potential complications. A person who is emotionally attached to another can not simply ignore the other's hardships. That's what it means to become attached. So in periods of hardship, there is an emotional need to direct resources (time, emotional tenderness, labor, money, whetever is needed) toward the needy person. Either the resources are spent, causing partner A to resent partner B for breaking the terms of Rule #2, or else the resources are not spent, causing partner B to resent partner A for not allowing aid to the needy third party to whom partner B is emotionally attached.

Then what about disease? In a closed relationship, the vectors are few and easily controlled. But when the relationship opens up to outside contacts, the pool of potential vectors expands to include those contacts, all of their contacts, all of their contacts, and so on recursively. In any sufficiently large population the pool quickly becomes prohibitively large to manage perfectly, and eventually something slips in through the cracks.

Every imagineable relationship arrangement, both open and closed, has already been tried and tried again throughout the millenia and across the planet. The fact that we as a species keep coming back to closed relationships as the standard speaks a lot to the wisdom of that choice over all the others.