If you know me then you know where I stand on reproductive health issues. This post is not to defend the Catholic Church's stand on artificial contraception, but to explain why she takes such a strong stance against it. I also hope to clarify some misconceptions on the Church's stance. If you wish to engage the Church on this issue you need to first understand where she's coming from and what motivates her. Maybe it will also help you evaluate the (f)utility of debating with the Church on this issue in the first place. This post is written with a lay (even irreligious) audience in mind, so I will dispense with the Bible quotes and Magisterial references.
It is no secret that the Catholic Church believes in the existence of God who created the universe. Duh. But corollary to this belief in a sentient and benevolent God is the assumption that everything He created has a purpose: nothing is random in God's creation therefore everything has to have been made for a purpose. So the Sun isn't just an amalgamation of cosmic particles brought together by gravity and heated by nuclear fusion; it was created to eventually sustain life on Earth. This belief system applies to all of creation, including the human body. Everything in the human body from the heart to the toenail you clip off has a purpose willed and designed by God. So far so good. No problem.
The problem begins when we start talking about the reproductive system. The Catholic Church believes that the reproductive system-- not just the womb and testes but also the pleasure-giving glans penis and clitoris-- have a dual purpose: to express mutual love and to procreate. The reproductive system was created to enable humans to express their mutual love for each other through sexual intercourse and to encourage procreation. Now take note of the "and". The Catholic Church's issue with contraception begins when that "and" becomes an "or". Artificial contraception, by removing any possibility of procreation, turns sexual intercourse into an exclusively love-making pleasurable affair. This, believe the Church, is contrary to God's will and purpose for creating the reproductive system.
But how about natural family planning? Or when one spouse is infertile due to natural causes or a needed medical operation (e.g., hysterectomy due to a tumour)? Won't sexual intercourse in those situations be divorced from the procreation purpose too, and therefore against God's will? Well, no. Natural family planning, by virtue of being natural, is part of God's plan: in God's wisdom He recognised the need for families to plan and space their offspring, but also recognised the need for spouses to make love, so He provided windows of opportunity to make love while vastly minimising the chance of conception. As for infertility due to natural causes or a needed medical operation, well, God had reasons for giving someone that affliction, and it definitely wasn't His intention to prevent spouses from expressing their love for each other. So in these cases any dichotomy between love-making and procreation was not man's will but God's, which is fine for the Church.
So the Church's real problem with artificial contraception is that man is divorcing love-making with procreation. In the case of artificial contraception, man wants the love-making part while eliminating the procreation part. Note that the same problem arises when man wants the procreation part while eliminating the love-making part, thus the Church's similar opposition to in-vitro fertilisation. Man cannot, should not, separate the expression of mutual love from the possibility of procreation. God can do it, but not man.
It is thus easy to see why no amount of medical, social, economic, democratic, etc. arguments or evidence will change the Church's position on artificial contraception-- they all pale in comparison to God's will and purpose for creating the reproductive system. Practical circumstances may mitigate the gravity of going against God's will through the use of artificial contraception (or in-vitro fertilisation, for that matter), but it is a sin nonetheless and bishops will be remiss in their duty if they tolerate it. So changing their stance on artificial contraception will require a change in their understanding of God's purpose for creating the reproductive system. It hasn't changed in 2,000 years, so it is quite unlikely that it will change any time soon.