Jesus never said anything about _______.
Such a person may call himself a "red letter Christian." That is, he wants to talk about what Jesus (didn't) say about the issue. Such a conversation isn't recorded in the gospels? Well, end of story for him.
There are many problems with this view. Let me stream of consciousness some out:
1. It's presumptuous to demand that only the Christ of Christianity can prohibit it when God spoke not only through his Son but also through regular people. It places an unwarranted wedge between God and his official leaders and is an anti-historical tone. Moses spoke the the abomination of homosexual acts (as well as other sexually sinful ones). Are there people today who would say that Moses isn't a recognized leader of God's Israeli community? Try floating that one by a Jew today. Paul spoke of the sin of homosexual behavior. I am aware of no scholar (even a flamingly liberal one) who denies the existence, the conversion and the apostolic ministry in the early church of the Rabbi Saul of Tarsus. Whatever the scholar today may think of him personally, he will admit that Paul was an early and influential church leader and that Christians believed him then.
Or do you not know that the unrighteous will not inherit the Kingdom of God? Do not be deceived. Neither the sexually immoral, nor idolaters, nor adulterers, nor male prostitutes, nor passive nor active homosexual partners, nor covetous, nor drunkards, nor slanderers, nor extortioners will inherit the Kingdom of God. (1 Corinthians 6:9-10)To say, "Moses and Paul have no authority to deliver binding revelation from God to me," is just arrogant. And where did Jesus say his was the only voice to be used in establishing Christian doctrine? Who are we to tell God how to write his Bible?
2. There was no foreseeable need for Jesus to be on the record about the issue. He preached primarily to a first century Jewish audience (that is to say, Second Temple Judaism). The Jews of the day wouldn't have remotely thought that homosexual behavior was legitimate. Even though some Jewish authorities denied Jesus they did not deny Moses. Hence, they would've taken Moses' Torah instruction to heart and condemned homosexual behavior.
It would be like me getting up in the pulpit Sunday and declaring that incest is sinful. I have no need to preach that Sunday because everybody in the audience would already know that. (Give it a few years and, given this society, it might not be a truth just taken for granted.)
The New Testament writers tended to write about things that needed correction. That is, we get Paul's views on things that people were messing up. I wish Paul said a lot more about everything but he didn't. He crafted his letters to fit the occasion of writing.
Jesus didn't have to talk about homosexuality because it wasn't a problem. He did have to address heterosexual divorce and remarriage because that was a problem in the Jewish community.
3. Besides, how do we know that Jesus never said anything about it? Maybe he did. Maybe he spoke about gentile sexual sins in passing but it just wasn't recorded in the Bible because the Holy Spirit didn't direct the gospel writers to write it. As John himself says,
Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written. (John 21:25 ESV)
There it is.