The problem with reincarnation is that the belief that our souls are enfleshed again in different forms dismisses any uniqueness of personhood. Not only does reincarnation treat the body as a shell or a cast-off and the soul as recyclable, but it completely ignores the part that our gender plays in our personhood because it has no understanding of the gender of the soul, if you will.
Our bodies and our sex are not incidental. Like John Paul 2 said, they are our “souls made visible.” When it is said that we are made in God’s image it means that they have something to teach us about God.
If our bodies are feminine it is because our spirits are feminine and a reflection of the side of God that reflects the gifts of the feminine: life-bearing power, nurture, reception of life, softness, acceptance, fierceness, loyalty, etc.
If our bodies are male it is because our spirits are male and reflect God’s strength and power, donation of life, enveloping protection and the call that a man seems to gravitate to so naturally to lay down his life for others.
Our bodies are not just houses for our souls, but they are our souls with flesh. It is important to realize the importance of this union and how disordered the separation which is called death is.
Our bodies are so esteemed by God that Christ went through the trouble of making sure that there will be no more separation of body and soul when He comes again. He Himself underwent death and resurrection so that our bodies would reunite with our souls and be healed of this separation once and for all in our glorified bodies.
The problem with reincarnation is that it denies that each person is a unique, once-in-a-lifetime unrepeatable gift to the universe.