Why do Christians believe that their god does not want people to have same-gender sex? What do they believe is God's reasoning behind it?

Because He has clearly said so in His inerrant word of the Bible.

Because it is against the design of God and it is rebellion.

1 Corinthians 6:9, 10 : "Or do you not know that unrighteous people will not inherit God’s Kingdom? Do not be misled. Those who are sexually immoral, idolaters, adulterers, men who submit to homosexual acts, men who practice homosexuality, thieves, greedy people, drunkards, revilers, and extortioners will not inherit God’s Kingdom."

Its because God didn't write the Bible, humans did. Those who pick out that verse and claim to follow the Bible truthfully, tend to pick and choose other verses to follow or not follow. For example, getting a haircut, getting a tattoo, wearing two different types of fabric or leaving your religion are considered sins. I'm not a Christian but people who are gay or trans are people too and should be treated as such. 

Actually the bible does not address same sex marriages.

Because back in Biblical times sex was for procreation only.  Since same gender sex cannot produce children, it was forbidden.