Is same-sex marriage a sin? Why?

Yes, same-sex marriage is a sin.

It goes against God’s created purpose for us as male and female and disobedience to God’s precepts and laws is sin.

So God created mankind in his own image,
in the image of God he created them;
male and female he created them.

Genesis 1:27

The practice of homosexual relationships in any way, including marriage, is an abomination to God. In his letter to the church in Rome, the Apostle Paul explained it this way:

Therefore God gave them over in the sinful desires of their hearts to sexual impurity for the degrading of their bodies with one another. They exchanged the truth about God for a lie, and worshiped and served created things rather than the Creator—who is forever praised. Amen.

Because of this, God gave them over to shameful lusts. Even their women exchanged natural sexual relations for unnatural ones. In the same way the men also abandoned natural relations with women and were inflamed with lust for one another. Men committed shameful acts with other men, and received in themselves the due penalty for their error.

Furthermore, just as they did not think it worthwhile to retain the knowledge of God, so God gave them over to a depraved mind, so that they do what ought not to be done. They have become filled with every kind of wickedness, evil, greed and depravity. They are full of envy, murder, strife, deceit and malice. They are gossips, slanderers, God-haters, insolent, arrogant and boastful; they invent ways of doing evil; they disobey their parents; they have no understanding, no fidelity, no love, no mercy. ³² Although they know God’s righteous decree that those who do such things deserve death, they not only continue to do these very things but also approve of those who practice them.

Romans 1:24-32

God created man and woman to enter into marriage so that they could be “fruitful and multiply” and fill the earth with future generations, i.e. children.  This is obviously impossible in a same-sex marriage. God in his infinite wisdom knows that children ideally need both a mother and a father to be properly and lovingly raised in a family. The family is also God’s basic building block for a joyful, safe, moral and just society.