I don't want to get dicey with the morality of what the Bible says in regards to slavery, because that would result in me either saying the Bible is wrong or incomplete, or make myself look really bad, neither of which I'm keen on doing.
As for homosexuality, according to my faith, God created man to be fulfilled by woman, and only by woman. The reason marriage is so important is because God made it to be a representation of his unity with himself; Father, Son and Holy Spirit. The act of sex is the covenant formed between a husband and wife to symbolize their love for each other, and before God. It bonds the two souls together. The act of homosexuality is immoral, in my eyes, for the same reason that pre-marital or adulterous sex is, because it is bonding your soul to somebody who you aren't in a covenant with.
Now to answer the inevitable question, why aren't you okay with two men or two women being married? Because God made man and woman to satisfy each other, and throughout the entirety of the Bible, from creation to a couple decades after Jesus' Crucifixion, teachers and Apostles said that homosexuality was immoral, and an illegitimate form of marriage. Simply, that is because it is not how God intended for it to be. I cannot answer further because I don't understand the complexities of men/women's souls and how they complete and satisfy each other. But thank you for your civility, I hope that clears it up in a way that is respectful to you or anybody who disagrees.