In the Matthew version (22:29), Jesus started with "Ye do err, not knowing the scriptures, nor the power of God." The Sadducees were different than the Pharisees in that they didn't depend on tradition for their beliefs, but on the Pentateuch, taking a Moses priority for all interpretation of the Old Testament. Jesus is saying, "Moses debunks your speculation," which was based on their rejection of the supernatural ("the power of God"), the liberals that they were. That worked nicely with the Pharisees, because the Pharisees thought people would be married in the afterlife. However, it didn't work with Jesus.
With the above background, consider the next part of Jesus' answer, because in it, He lays out some detail in the definition of marriage that is helpful in today's discussion. I watched a debate on same-sex marriage between Douglas Wilson and Andrew Sullivan. Sullivan, who claims to be married to another male, claimed that Jesus had nothing to say about it. That wasn't true, but it is especially false as we consider what Jesus said about marriage and procreation. Jesus Himself said that marriage related directly to procreation. The same-sex supporters say procreation is not a prospect of a marriage definition, because you've got some 'heterosexuals who can't or are past the point of having kids.' Let's just listen to Jesus in the Luke edition of this story (20:34-36):
34 The children of this world marry, and are given in marriage: 35 But they which shall be accounted worthy to obtain that world, and the resurrection from the dead, neither marry, nor are given in marriage: 36 Neither can they die any more: for they are equal unto the angels; and are the children of God, being the children of the resurrection.
First, what is Jesus saying? One, people in this world of these temporal bodies marry (v. 34). Two, those who make it to the world to come in those glorified bodies after the resurrection of the dead will not marry (v. 35). Three, they won't marry because they won't die any more, being equal to the angels (v. 36).
You've got to look closely to follow all of Jesus' argument. It's not hard, but you've got to do some thinking. A surface understanding blew the Sadducees away, but this section also deals nicely with the reason for the definition of marriage, coming from Jesus. Angels don't marry. They were created all at once and none of them die. Since none of them die, they don't need to procreate. People in the world to come, who make it there (because they're saved), will not be married either because they won't die. Get it? Jesus explains that people marry because people die, so it is necessary to procreate. People who die need to be replaced. Procreation is what replaces them. This is replenishing the earth. This happens from a man and a woman only.
Second, how does this apply to the definition of marriage? Angels don't marry because they cannot procreate. Men don't marry men and women don't marry women because they can't procreate. A fundamental part of marriage in general is that it must be between a man and a woman, because only they can replenish the earth. Only a man and woman can procreate. If people were like angels, they would not need to marry. This is what Jesus is saying. At a root level, marriage must be between man and a woman based upon a fundamental understanding of procreation.
Now remember, Jesus is the Creator (John 1:3; Colossians 1:16; Hebrews 1:1-3). We've been endowed by our Creator with certain inalieanable rights. Do people have the right to marry? Yes. By definition of the Creator they do. And our Creator said that procreation is one aspect of the definition of marriage. Men and women, speaking of them in general, marry in part because mankind can only procreate with a man and a woman. Procreation is Jesus endorsed, Jesus originated, legitimate, authoritative argument against same-sex marriage, based upon Luke 20:34-36. Procreation eliminates same-sex marriage.