I think it's a combination of things. The gospel is offensive to many people. Even the cross of Christ, which is the very center of our beliefs, is a stumbling block to millions. Well, even Jesus Himself is a stumbling block to many. The scriptures describe Jesus as, “A stone of stumbling and a rock of offense” (1 Peter 2)
The fact that people are driven away isn't necessarily a bad thing. Many assume that if people get upset with them then they must have done something wrong. Sometimes, it's the opposite. Sometimes they did something right.
People want to remake Jesus into their own image. They want to revise all He said and did to fit their own ideal. They try to conform Him to themselves instead of conforming themselves to Him.
When we tell people that homosexuality is wrong and immoral and sinful as God says, it threatens people on a couple levels. One their sense of freedom is threatened. Two, their belief that man is basically good is threatened as well.
People often argue for gay marriage on the belief that it's about equality because they're afraid that their "freedoms" to make their own choices will be outlawed too. They want "freedom" to do whatever they wish but their definition of freedom means "the freedom to make choices without any negative consequences." They seek to suspend the natural, built-in consequences that God place in His moral law. They are inescapable. We all face such consequences soon or later.
Regarding the whole "Jesus never spoke about homosexuality or condemned it" argument people are making on this post, I think Pastor Kevin DeYoung gives an insightful answer -
"...it’s hopelessly anachronistic to expect Jesus to directly address all our contemporary concerns. Jesus never said anything explicitly about child abuse, domestic abuse, bestiality, abortion or dozens of other sins. He never preached a sermon on homosexuality because no one in his circles by any stretch of the imagination would have approved of homosexuality under any circumstances.
"...the fact is Jesus spoke about sexual sin often. He warned against lust and infidelity. He confronted the woman at the well. He told the woman caught in adultery to go and sin no more. Likewise, Jesus condemned the sin of "porneia" (Mark 7:21 [3]) which is defined by a leading New Testament lexicon as “unlawful sexual intercourse, prostitution, unchastity, fornication” (BDAG).
"James Edwards states that porneia “can be found in Greek literature with reference to a variety of illicit sexual practices, including adultery, fornication, prostitution, and homosexuality. In the OT it occurs for any sexual practice outside marriage between a man and a woman that is prohibited by the Torah” (The Gospel According to Mark [4], 213).
"It’s misleading to suggest that Jesus had no discernible opinion on homosexuality or that sexual sin was not an important concern for him." - Kevin DeYoung