"You need to defend the assertion that not ordaining women to the priesthood somehow makes the Church patriarchal."

Just take a look at any photo of a Catholic liturgy, especially at the Vatican.  If this is not patriarchy, then what is it?

We believe that the Church is "one, holy, catholic, and apostolic."  
Do we believe that the Church is, in addition, patriarchal?  No, but this is what the patriarchal priesthood reduces the Church to be: an artificial and obsolete patriarchy.

The complementarity of man and woman is for reciprocity and interpersonal communion, and was never intended to reduce human relations to patriarchal gender stereotypes.  See JP2's "Theology of the Body," links included here:

Religious Patriarchy ~ Annotated Chronology of Key Events
http://pelicanweb.org/CCC.TOB.html#CHRONOLOGY

We celebrate "Corpus Christi," not "vir Christi."