They used to be honest and say that women cannot be ordained because women are inferior to men. See, for example, Aquinas' Summa Theologica,  Supplement, q39 art 1, on the question, "Whether the female sex is an impediment to receiving Orders?" He says, "Since it is not possible in the female sex to signify eminence of degree, for a woman is in the state of subjection, it follows that she cannot receive the sacrament of Orders". That, FC, is sexism in a nutshell. Now, they say that this argument is invalid, but in fact, it is still trotted out. They call it "complementarity" and "ontological differences", but it's still just "women are inferior to men".

"Liberal, secular, atheistic humanism" has nothing to do with it. It's sexism, pure and simple. As I said, they used to be open about it, now they are just as sexist, but pretend they aren't.