As a Christian, you cannot pick and choose which parts of God's word apply to your life. Either all of it does, or none at all.
There are clear-cut verses that state that homosexuality is an abomination such as 1 Corinthians 6:9-10, Leviticus 18:22, and Romans 1:24-32. I would suggest that anyone who claims the blood of Christ read those verses and see for themselves that homosexuality is a vile and grievous sin against God, thus making homosexual marriage an abomination as well.
God said in Genesis also that "a man will leave his father and mother and cleave to his wife and they shall be one flesh." Where do we see homosexual marriage in that? If God approved of homosexuality, He would have created it as natural and healthy and would have provided a way for homosexuals to procreate. But that is not the case. God did not say, "A man and his husband" or "a woman and her wife."