I think he was primarily speaking of the biological nature of the female half of the human species. They are built to care. In the same way they care for children, they care for the material in this world. Women are considered frivolous for this reason. They care about diamonds and pearls, they care about aesthetic beauty, they care about every last facet of a man so as to weigh his worth. They care about intelligence, strength, power, skill, etc. Caring cuts down to the bone of women whether they care for children or for money or material locations (Paris, etc)

It is this tendency to care for things that gives them desire, and, as the opposite of loyal (man), women are primarily concerned with themselves and their own interests. There is no true loyalty in the mind of a woman. There is only self-interest. Women see the weak and defective, and they care for them and then walk away. In their natural habit they would never let a weakling have sexual intercourse with them. This is the fundamental driver of evolution. Women are the gate keepers of sex. This is why Nietzsche considered them higher life-forms than men. They are so self-interested and manipulative that, on a certain level, they do not see others as human beings, they see tools to get things they want. A terribly feminine woman just wants admiration (something they care about) once they've got acceptance in a tribe.

They just want to be seen as a grand, superior life-form that is higher in rank than those around it. The rank matters because it is a measure of worth, and worth is something women care about. It's just will to power in action. Women use their ability to care to see every last bit of another human being, and they manipulate others to get what they need. Women don't even feel negative emotions in the same way that men do, their amygdala activates differently, so they are better at emotional recollection than emotional experience. It would be disadvantageous for women to really understand human emotion as it would be retard their ability to freely manipulate and use. For men have historically been nothing more than tools to women. If you pay attention, you'll find that women selfishly have kids even though they're well aware life is hell, and someday their children will suffer over what they've done.

Women are constantly leaving men for something superior. It's sad but true. You, of course, get exceptions to rules, but it's rare. This is probably what Lanza meant by selfish. They are not built that way through society. It is in their blood and bones to choose the superior life form and run with it. This is why so many mass-shooters hate women. They are aware of what they truly are, and it takes a sufficient amount of time in isolation to realize it. This is what Adam Lanza saw in his mother. "I want what I want, and you're coming whether you want to or not." This is what Adam thought about his mother as she forced him onto this earth, forced onto him her "love" so that he became weak in a brutal society, and then forced him out of his cocoon.

Women really are selfish. My father has seen it. I have seen it, and Adam Lanza has seen it... It can't be helped. They are highly evolved lifeforms that perpetuate the species, and they must be fundamentally cruel so it is driven forward.