So the Church is a woman with a female body and a male head?  Read JP2's Theology of the Body.  It clearly explains that the great mystery of Christ and the Church cannot possibly be reduced to a patriarchal analogy.   It also explains that human bodies are male *or* female, but human persons are male *and* female;  Eve is in Adam as much as Adam is in Eve.  See also the Catechism of the Catholic Church (sections 239, 370, 2779) which clearly explains  that God cannot be reduced to patriarchal gender stereotypes.  Please do your homework, rather than just pushing patriarchal gender stereotypes manufactured by human hands, not God's.