Reddit mentions of Patterns of Culture

The short answer is probably around the beginnings of sedentary life. Eight to twelve thousand years ago depending on where and who you are asking.

A longer answer requires an understanding of inter-generational wealth transfer. Simply put: if you have a certain social status that is dependent of some quantity of capital, any of that capital you expend to raise a child had better be spent on a child you know is yours genetically. In a society that practices honor killings a woman's value relies her her virginity and fertility. Virginity because controlling her sexuality is the sole way for a male to guarantee that his children are his, and fertility to provide her husband with children. (In pre-industrial societies children are economic assets, unlike today, because they can work for you.)

Ruth Benedict and Margaret Mead were among the first anthropologists to openly observe that societies with little economic stratification were much more sexually permissive than societies with a great deal of wealth and poverty. A good thought experiment is to consider "The Garden Of Eden": If the environment were such that no one had to do anything other than pick food from the trees to survive, then it wouldn't matter whose children are whose because no one has to put any effort into their survival.

By contrast imagine today's society with no CPS or orphanages ect, and the only way to achieve any material success is to be blood related to someone with a lot of money. Then it matters very much whose children are whose.

Now back to OP's original question: "Honor Killings" killings exist in societies where social status is based on economic inequality, and where any kind of wealth transfer requires some kind of blood relation. These societies couldn't have existed before the development of some kind of agriculture/aquaculture which was between 8,000 to 12,000 years ago depending on where and who you ask.