Homosexuality is against the eternal nature of God's plan. God's plan is the plan of happiness. Going against God's plan brings less happiness to the soul of man. For this reason, homosexuality is considered an abomination since it is in direct opposition to his plan. God has commanded:
Genesis 1:28
28 And God blessed them, and God said unto them,
Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
Genesis 9:1
1 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.
How can one be fruitful and multiply and replenish the earth without doing so with the opposite sex?
Adam was legally married to Eve by God and it is recognized in this verse:
Genesis 4:1,25
1 And Adam knew Eve his wife; and she conceived, and bare Cain, and said, I have gotten a man from the Lord.
It is against God's law to have sexual relations outside of marriage and that marriage must be between those of the opposite sex:
Ephesians 5:3
3 But fornication, and all uncleanness, or covetousness, let it not be once named among you, as becometh saints;
Jude 1:7
7 Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.
Leviticus 18:22
22 Thou shalt not lie with mankind, as with womankind: it is abomination.
Romans 1:24-27
24 Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves:
25 Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen.
26 For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature:
27 And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompence of their error which was meet.
It has been revealed in these latter-days that the covenant of marriage can be an eternal bond if done through the sealing power of the holy priesthood and according to will of God. Marriage is an eternal union for those who obtain the sealing.
Doctrine and Covenants 131:1-4
1 In the celestial glory there are three heavens or degrees;
2 And in order to obtain the highest, a man must enter into this order of the priesthood [meaning the new and everlasting covenant of marriage];
3 And if he does not, he cannot obtain it.
4 He may enter into the other, but that is the end of his kingdom; he cannot have an increase.
God created man and woman so that they could come together in an eternal union of happiness. Anything outside of this is against God's law of happiness that he ordained for mankind.
Alma 41:10
10
Do not suppose, because it has been spoken concerning restoration, that ye shall be restored from sin to happiness. Behold, I say unto you, wickedness never was happiness.
