Patient's Dillema and the Concept of Suffering

When I took a Morals and Ethics course in undergraduate school, I was struck by a pro-abortion argument that was a little strange and different to me.  I never personally wrestled with it as a serious argument to why abortion should be OK, but I could definitely understand how others could be confused by the dillema - one that mostly targets cases of rape and incest.  I'm going to call it the "Patient's Dillema" even though there is probably a better name for it.  The argument goes as follows:

"What if one day you woke up only to find out you were in a hospital bed - not of your own choosing but because someone had abducted you in your sleep, tied you down to the bed, and connected your liver to a famous organist.  This organist is lying next to you in a coma, and his liver is unable to function on its own.  Doctors tell you that they can fix his liver, but he will have to be attached to your body for 9 months.  Are you morally obligated to allow him to be connected or can you unhook him and let him die?"

Most of the people in my class felt that you absolutely were under no obligation to let him stay connected - especially because it had nothing to do with you and you were placed in a situation that was not your fault at all.  I was Protestant at the time, but I argued that you had an obligation to protect his life because it was life.  Obviously being Catholic I would say that the Church clearly teaches that we would be under that obligation.  

But the deeper question is WHY?  Why do we have that obligation?  On one hand, I was correct as a Protestant, that life is important and we must do whatever it takes to protect it.  But, on another hand, and I think on a deeper level, we have to understand something about suffering.  We look at instances like someone being raped or someone being attached to an organist as an example of when we cannot expect someone to provide for this life because they themselves have to suffer and, in our modern society, suffering is a terrible thing that no one should have to do at any cost.  We have really lost the sense of understanding about how important suffering is, and that is actually a blessing from God that we do suffer.

That can be illustrated in the easy sense of being burnt.  When we touch a hot stove, we suffer.  That teaches us not to touch the stove. But, it goes much deeper than that.  Suffering is part of our human nature, and when we suffer we participate in some ways in the suffering of Christ and are brought closer to God.  Reading Pope John Paul II's encyclical on suffering or works like St. Faustina's diaries where she is told to suffer by Christ in certain situations can really help us understand the positive side of human suffering.  On top of that, we have scriptures where Christ tells us that we must suffer, that those who suffer are blessed, St. Paul tells us how he rejoices in his sufferings, and Peter tells us that we will have to suffer to become more like Christ.  Look at the early martyrs of the Church in the Book of Revelation.  Through their suffering, the Church prevailed over the world.

Anyway, I guess my point is that suffering is not something that must be avoided at all costs, as our modern society tells us.  If we realized the important value of suffering, we can understand that protecting life takes a precedent over protecting ourselves from that suffering.