Societies have encouraged female predispositions or instincts throughout history.

The way people think about instincts is wrong. In higher animals they are not like a program that a robot carries out. Since they are genetic in origin they are fixed, they can't be altered by socialization but the way they are acted out can be.

It's helpful to think of instincts as predisposition. A spider has a predisposition that when trigger by the environment causes a cascade process. First to build a thread then that thread triggers a new predisposition so on and so forth until a web is built. The reason that the spider seems to be analogous to a machine isn't because it's a little robot it's because it is a very simple creature. It gets very limited information from the environment on which it's predispositions can be acted on.

The same process takes place in humans but they take in a lot of information from the environment. That creates a lot of memories of environmental conditions. The brain then sorts out if immediate stimulus or memories should be acted on based on intensity. If the memories are strong environmental conditions may be ignored. What makes memories strong are emotional responses. Those emotional responses are a cascade of memories that build on each other.

In the past the female instinct to mate and reproduce was socially reinforced by the social construct of female intuition. Basically conditioning women to feel and not think to deeply about the cost of motherhood. Today where society is less interested in reproduction females are taught that their instincts are special. That intuition is their special gift that adds diversity and value in the work place which diverts emotional energy away from reproduction. This is an example of how the same predisposition can be used for opposite ends. In the latter case the emotional energy normally devoted motherhood is transferred to a career. The career becomes an infant figuratively.

That females are duplicitous is an oversimplification. In any social mammal that is dimorphic the weaker sex is at a biological disadvantage possibly leading to runaway dimorphism. Some of the mechanisms that prevent this are physiological some behavioral. Anyone interested in the topic should study cryptic sexual conflict. One example is the ability of female bodies to reject or accept sperm from multiple sexual partners. Even female orgasms can be part of this process. The point is that cryptic and duplicitous should not be confused because often females are not even aware of what their complex instincts are doing.

As to covetous that is also more complicated. Society having taught women to follow their instincts accordingly to social influences shouldn't be surprised when they do. Women having been discouraged to think deeply are not so much covetous as obsessed with instinctual fairness and resource hording. Institutional fairness is confusing because in nature there is very little productivity and a general focus on resource consumption. It's part of the natural conditions that make us adapted to a fast lifestyle for an easy but unstable environment. Men have been socially conditioned to be productive for the slow lifestyle and harsh but stable environment civilization requires. Fairness instinctually means getting a fair distribution of available resources not based on productivity.

Judging people by their innate and immutable characteristics is a dangerous path to take. Better to judge them on their behavior in relationship to their instincts. Neither men Nor women are instinctually designed for civilization. In the past religion bridged the gap between instinct and the abstract civilized world. Wokeness is currently filling that gap but it isn't evolved. It's in the formative stage and is maladaptive. Social structure are very complex and should receive a good deal of consideration having evolved for ten thousand years.