Here, it's important to understand that there were different kinds of Old Testament law. The Old Testament contained ritual (ceremonial), sacrificial, civil and moral law. Jesus affirmed its entirety, yet brought to an end the ritual and sacrificial law by fulfilling them.
The civil law was established to facilitate the affairs of state for Israel through a direct relationship with God. It was stricter because God governed Israel directly from heaven via revelation through Moses and the Prophets. Though some of the wise principles found in that law are still in common practice today (such as the distinction between first degree murder and manslaughter), the stricter penalties no longer apply because we no longer have that kind of direct oversight by God.
As for the ritual and sacrificial laws, Jesus fulfilled them by His life and death. He became the sacrificial Lamb and fulfilled all of the matters to which such laws pointed.
The moral law, however, is a reflection of the very character of God.
The moral law, however, is a reflection of the very character of God. Consequently, moral law is as unchangeable as is the nature of God. As such, it will continue throughout eternity. Jesus kept the moral law perfectly (John 8:46; 2 Cor. 5:21; Heb. 4:15, 7:26, 9:14; 1 Pet. 1:19, 2:22; 1 John 3:5) in order to reflect His Father's character. His perfection also revealed His divinity and pointed to a future that He would give to those who accepted the only means by which that perfection could be applied to man; His sacrifice on the cross (Acts 4:12; John 8:24, 14:6).
Historically, Jesus didn't need to comment on homosexual behavior. In first-century Judaism, there was no debate about its sinfulness. He would have been preaching to the choir.
The "Jesus never mentioned it" argument assumes that only the words of Jesus are divinely inspired. This flies in the face of hundreds of Old Testament prophecies that have already been fulfilled. The mathematics of probability conclusively demonstrates that the Scriptures must be divinely inspired.
The "Jesus never mentioned it" argument also ignores Jesus' own witness to the divine origin of sacred Scripture (see Mark 12:35-36) as well as that of the apostles (see Acts 1:16; 1 Thess. 2:13; 2 Tim. 3:16-17; 2 Pet. 1:20-21, 3:15-16).
Every mention of homosexual behavior in the Bible is thoroughly condemned in both the Old and New Testaments (see Lev. 18:22, 20:13; Rom. 1:18-32, 1 Cor. 6:9-11; 1 Tim. 1:8-11; Jude 1:7).
The original Greek and Hebrew texts are crystal clear on this. In fact, the apostle Paul waved a red flag on this very subject when he took the words of prohibition for homosexual behavior from Leviticus 18:22 (mishkav zakur) that had been translated by Jewish scholars as arsenos koites in the Septuagint (the earliest Greek translation of the Hebrew text, about third century B.C.) and used a conflated form of them in 1 Corinthians 6:9—arsenokoitÄ“s—in speaking about the sin of homosexual behavior. According to New Testament scholar Richard Hays, it was the first time in the history of koine Greek (the Greek of the Bible) that such a word was used. In essence, Paul coined the term to alert readers that he was referring to the same prohibition found in Leviticus.
Nowhere in Scripture and nowhere in biblical history until the last century has homosexuality been thought of as an inborn, natural and immutable orientation. The Bible only speaks of "behavior," not "orientation".
Many activists claim that Jesus didn't use the word "homosexual" because He was unaware that it was supposedly a holy and healthy orientation that was both God-ordained and God-approved.
Are we to believe that the divine, omniscient Son of God was unaware of anything? The idea is ludicrous. It also flies in the face of the fact that many in the Greek world of Jesus' time did believe that homosexuality was an orientation, a fact that Jesus would have known quite well even if He hadn't been omniscient.
The world's top scholar on the original translation of these passages (Dr. Robert Gagnon) says the concept of homosexual orientation was not wholly unknown in the Greco-Roman milieu. He also asserts that there is absolutely no evidence that modern "orientation theory" would have any impact on causing Paul to change his strong negative valuation of homosexual practice.
Finally, homosexual behavior does not fit the stated purpose of sexuality in the Bible, which is heterosexual and monogamous. Scripturally, human sexuality has been designed to be expressed solely in a one-man, one-woman marital covenant. (See Gen. 1:27, 2:23-24, 5:2; Matt. 19:4-6; Eph. 5:31).
So, does the possibility that Jesus never mentioned "homosexuality" in the Bible create an excuse for homosexual practice? In the very strong words of the apostle Paul, me genoito, "May it never be!" (Rom. 3:4, NIV)."
Read more on Dr. David Kyle Foster here.