I don't think your argument follows very well.  To pretend that male and females don't differ in substantial ways requires one to ignore so much scientific findings.

You argue that in order to view man as integral personal subjects one MUST ignore their differences in body.   That's in fact just the opposite of viewing them as "integral personal subjects."

The pope precisely took a far more integral view of our humanity and our natural differences than you do. 

Can you imagine the following. 

Let's say that 250 years ago there was a movement to treat men and women's pronounced physiological differences as nothing but surface matters, stopping at the external organs and casting their complementary aside.

Then imagine the finding of cellular differences using "microscopes"...just take the sperm and the egg.  And then that would be cast aside. 

Then years later imagine detecting the complementary antibody action of women in the presence of sperm.  Amazing.

Then imagine genetics!