Q: I hear that Jesus never said anything against homosexuality.
A: Jesus never singled out homosexuality in his teaching; but did clearly confirm his support for the Mosaic Law which did condemn the practice:
17 “… I did not come to abolish the law of Moses or the writings of the prophets. No, I came to accomplish their purpose. 18 I tell you the truth, until heaven and earth disappear, not even the smallest detail of God’s law will disappear until its purpose is achieved. 19 So if you ignore the least commandment and teach others to do the same, you will be called the least in the Kingdom of Heaven. …-Matthew 5:17-19 NLT
The following are 2 passages in Leviticus (part of the Law of Moses) which do specifically teach against it:
22 You shall not lie with a male as with a woman; it is an abomination.-Leviticus 18:22 ESV
13 If a man lies with a male as with a woman, both of them have committed an abomination; they shall surely be put to death; their blood is upon them. –Leviticus 20:13 ESV
Fact is; Jesus lived in 1st century Israel and the Law of Moses was still in force as far as the Jewish religion and nation was concerned. With that in mind, he would not need to speak about it, unless he had a different opinion. Instead, he clearly made a point of supporting the Mosaic Law.
Later when Christianity spread into the Greek and Roman culture, where homosexuality was a common practice, the Apostles made it clear that homosexuality and other forms of sexual immorality should not be part of the life of Christians: Acts 15:20 defined that the new gentile Christians did not have to follow all of the Mosaic Law but did have to abstain from anything connected to idols, blood, strangled meat, and from sexual immorality which included homosexuality. Later the following scriptures did specifically address homosexuality along with other forms of immorality and violations of God’s law: Romans 1:26-28, Jude 1:7, 1 Tim.1:8-11.
Note: the death penalty (which was in the Mosaic law specifically for the nation of Israel) was never supported in the New Testament teaching. Also, those who practiced any kind of immorality including homosexuality and any other violations of God’s law could receive forgiveness if they accepted Jesus and turned away from their sinful lifestyle:
9 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 men who practice homosexuality, 10 nor thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers will inherit the kingdom of God. 11 And such were some of you. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God. -! Corinthians 6:9-11 ESV