I’m going to try and present the Church’s reasoning as best as possible (if I am completely off the mark, someone please correct me.), but I might find it difficult to keep secular and theological arguments separated, so bear with me.
The church isn’t necessarily fighting same sex marriage itself. It is fighting the legal redefinition of marriage. Previously, marriage (in the civil sense) was defined as being between a consenting man and women, in which case, procreation was possible (at least, in the vast majority of marriages, not as a condition of the marriage, but as a result). To be extremely simplistic, a man and woman agreed to marry because they wanted to live together (Culturally, this implied that they were “in love”. Theologically, this meant that they had received the Sacrament of Matrimony and their relationship was a reflection of God’s love), and they agreed that they would have responsibilities towards any child that they procreated. So, we can see that even in the previous legal definition of marriage, the two aspects of a marriage relationship that the Church requires are met: procreative, and unitive. The couple express their love before either God or a court, and agree to accept children given to them by God, or to have mutual responsibilities towards any children that result from the marriage (whether intentional or by accident).
Now, same sex marriage is attempting to redefine marriage. Proponents want marriage to be between any two consenting adults, whether heterosexual or homosexual. Now, obviously, a homosexual couple cannot procreate. This is something that gay marriage proponents don’t stress or say very often. They simply cannot produce children (adoption is a different story). Now, what does that do to the definition of marriage? No longer does a couple have to physically be able to procreate. So, now there is only one aspect of marriage that is preserved: unitive. Obviously, to the Church, this is unacceptable (the Church also teaches that homosexual union is not unitive either). Culturally, this says that all that is needed for a couple to be married is that “they love each other” (Side note: I am fully aware that legally, all that a marriage liscence does is grant certain legal benefits (hospital visitation rights, right to file taxes jointly for a smaller tax burden). However, I am referring more to the cultural notion of marriage. In most cases, people don’t get married to get these benefits. They get married because they “love each other”). Now, proponents of same sex marriage will disregard the following argument as illogical and irrational: If all that is needed for “marriage” is a mutual agreement of affection and cohabitation, where do you stop? If two men can marry, why not two eight-year old children, or one man to fifteen women, or a woman to her pet dog? Can’t children both agree that they “love each other” and want to get married (as absurd as this sounds, a previous poster mentioned that there are a growing number of learned individuals who are making similar arguments, just with pedophiles and their victims (that is, attempting to prove, psychologically, that they are able to “love” each other))? If a man loves 15 women, why not get married to all of them? If a woman loves her pet dog, and she believes the dog loves her, why can’t they get married (many philosophers and psychologists can also prove this)? It is, indeed, a slippery slope, because there is nothing objective (such as the necessity or possibility of procreation) to stop a runaway freight train of subjective feeling or reasoning.
And therein lies the fundamental fallacy and danger: When you reject objectivity, everything is fair game, because then everything becomes “Well, I feel this way, and alot of other people feel this way, therefore, it must be right”.