Euclid's Geometry is based on five axioms. These axioms are used to build the whole system. If you change one of the axioms (i.e. you say "two parallel lines CAN intersect") then the ENTIRE system changes, and it looks COMPLETELY different than Euclidean Geometry.
You can change one of the axioms, but the change echoes throughout the system, producing a completely new system.
Marriage between a man and a woman is an axiom of our society. It is assumed to be true and everything hinges on that as a foundational principle. There are a few other "axiomatic" principles that our society is founded on. The Church notes that a just society is one in which:
1) the dignity of every human life, from conception to natural death, is honored
2) religious freedom is granted
3) the right to work is respected
4) marriage is between a man and a woman
IF YOU STOP UPHOLDING THESE VALUES...THE SYSTEM CRASHES...DEMOCRACY EXISTS NO MORE
Some people think the Church is against same-sex "marriage" because the Bible and the Church are against same-sex sex. The Church is against same-sex "marriage" because the Church knows the types of decisions that bring societies crashing down - and one of those would be a redefinition of what marriage is.
That's why the Church says:
"If, from a legal standpoint, marriage between a man and a woman were to be considered just one possible form of marriage, the concept of marriage would undergo a radical transformation, with grave detriment to the common good." (Compendium of Social Teaching, paragraph 228).
Here's the point - we're not saying, as Catholics, that society needs to listen to us because God is great and "you all need to do what God says"...
The Catholic Church says, as a political advisor, IF YOU CHANGE YOUR UNDERSTANDING OF MARRIAGE, YOUR SOCIETY WILL NOT ENDURE
If you change one of the foundational axioms, you change EVERYTHING...and when you change an axiom, what you soon have is a system that looks NOTHING like what you had before