Function of testosterone in women and estrogen in men
As you know by now, both males and females have testosterone and estradiol. Of course, their levels are different in each sex, but both hormones are important to males and females. A human male with zero blood concentration of estradiol or a human female with zero blood concentration of testosterone wouldn't be possible.

Here are some famous examples:

Role of testosterone in human females:


Increase libido1,2
Modulate physiology of vaginal tissue3


Role of estradiol in human males:


Help to regulate spermatogenesis4
Reduce bone loss5