There is simply no good reason women should not be eligible for the priesthood.The strongest reason I can give you for why women cannot be priests is that priests act in persona Christi capitis -- in the Person of Christ the Head.
It's true that, in baptism, we have all put on Christ and that he has incorporated us into his Body, and in that sense we can speak about everyone in every vocation acting in persona Christi. But the Church always speaks specifically of the priest acting in persona Christi capitis. The body of the Church is just that -- the body, not the head. Christ alone is the head, and the priest has the unique vocation of representing the unique headship of Jesus Christ.
Why can’t a woman represent the “unique headship of Jesus Christ”?