The placenta is a miraculous organ. It develops from the same cells your baby does (some cells become an embryo, while others form the placenta). The placenta provides baby with oxygen and nutrients, filters waste, and serves as a barrier against germs. It's essentially your baby's life-support system, and is the only organ created and discarded by the human body. It's also f*cking disgusting. Out of sheer curiosity, I asked dads to describe what a placenta really looks like.
I don't remember too much about delivering my placenta. I think I sneezed, and it came out. However, I vividly recall the biology lesson my midwife gave both me and my husband. She held up what looked like a bag of raw meat from its plastic science laboratory bin, and showed us the sac our baby had been in and the cord that had been the conduit between her and the placenta.
My husband took a picture. Knowing that my sister and I are big weirdos (and that I'd been sharing all my bodily changes over nine months), he texted it to her. When I recently asked him to describe it, he called it, "The second most disturbing thing a man sees when his wife has a baby." He still refuses to tell me the first.
In general, I think moms are more likely to view their afterbirth fondly. After all, their body manifested it into existence and it sustained the precious life growing inside them. Dads? Well, dads have a take that's a little more, shall we say, objective.