Their position is true because the pope, his cardinals, his bishops, his priests, and the magisterium say so. Contraception denies birth, and contraception can never truly work unless using the rhythm method so taught by the holy roman and apostolic catholic church. If the pope says so, its always true.
In the Church's view, a thing is good to the degree that it approaches its final cause. For instance, a door is supposed to cover an exit or entrance. If a door has a bunch of holes in it and lets rats and stuff in, that would be a bad door since it is not fulfilling its purpose, which is its final cause.
Similarly, human sexuality has a final cause: the procreation of children. While it is true that sex is secondarily for emotional connection between spouses, etc., this does not justify obfuscating the primary purpose (final cause) of sex (procreating), which is the very thing contraception does.
Obviously, this is not all that can be said about the Church's position on this issue, but I can't hope to adequately summarize the literally millions of pages which have been written by brilliant philosophers and theologians about it. Yet, the many arguments given by philosophers, theologians, and apologists, of which the argument given above is but a truncation, do serve to justify the Church's position on contraception.
P.S. The Church's position does not come just from divine revelation, but from natural law and reason. Thus, everyone who cares to deeply think about and study the issue can arrive at the Church's conclusions to a large degree, as various pre-Christian philosophers did who had no idea a Catholic Church would come around and make a policy about it.
The Roman Catholic Church's contraception policy is not justifiable. When they bar a women from doing some thing that she wants to do with her own body under her own power, that is wrong. Every woman should be entitled to contraception as to prevent an unwanted pregnancy, because that happens too oftens these days.
The Roman Catholic Church's contraception policy is out of date and not justifiable. I'm a Catholic myself and disagree with it. Contraception is very important and should always be the choice of the couple involved. Proper use of contraception avoids unwanted pregnancies and prevents the transmission of sexually transmitted diseases. It is time for the church to update their ancient policies and join the 21st century.