First of all, the biblical teachings about homosexual sex are far more knowledgeable than many would think. We moderns like to think we are so much more sophisticated than those who lived before us, and this is especially so regarding the ancients. This simply is wrong, and very wrong regarding ancient societies. The Hebrew peoples, later the Israelites, and even later Judaism were familiar with all kinds of sexual practices which were indulged in and celebrated by many of the peoples surrounding the ancient Hebrews and Israelites. (Technically speaking, Israelite is a later designation for the Hebrew people, as the term Hebrew - in Egyptian and Akkadian, habiru or hapiru - is earlier.) Given the Hebrew/Israelite experience with a sovereign God who claimed to be the one true God who wanted to be revealed through a unique relationship (covenant) with a unique people (community), they developed a unique clarity regarding what sexual practices were intended by this God, and what ones were not. The Exodus, Deuteronomy, and Leviticus passages prohibiting homosexual practice are very clear and are far beyond simply being a sheltered society's inability to view it apart from marital infidelity, or to view it as no more consequential than directions for eating or instructions for acceptable clothing fashions around 1000 BC. Sexual confusion and disobedience are viewed as particularly destructive to individuals and society. They are more than incidental to human customs, and are viewed as a denial of God as the Creator and are a defiant rejection of the inviolable order of creation.
Paul picks this up in his writings, especially in his letter to the Romans. It is very likely (as indicated in I Corinthians 7) that he had access to some kind of pre-Gospel version of Jesus' teachings. In these he finds Jesus reaffirming the sexual code in the Torah, particularly in Jesus' words on marriage, where Jesus frames marriage in terms of the created order, and the image of God the Creator ("In the beginning God created them male and female...." Matthew 19:4). Paul expands the idea that homosexual practice is a clear and graphic illustration of human arrogance before God, where mere humans deny the authority of God as the creator of all and seek to subjugate the created order to their own will and whim. This is for Paul the nature, result, and judgment of sin.
The early Christians, the apostles, Paul, Jesus, the Prophets, Jews, Israelites, Hebrews, and even Abraham and Sarah were all familiar with peoples and opinions that approved, promoted, and celebrated homosexual practice in various ways: as religious service, partnerships (both short term and lifelong), extramarital expressions, philosophical lessons, and plain old raw animalistic lust. In Jesus and the early church's time, there even was some discussion among the Greeks regarding the idea that homosexual relationships were superior to marriage, since women were associated with marriage and women were thought to be greatly inferior to men (in Greek society). Romans, who viewed marriage more as a contractual agreement (an idea central to the later European view of marriage), did not see any benefit to two males marrying, since women usually transferred property rights. As you can see, our modern experience is in no way more informed or enlightened than Paul, Jesus, or the ancients.
The biblical texts speak from a clear understanding of the God who spoke personally to Abraham, Isaac, and Jacob; called out and covenanted with a despised violent mercenary slave people; and spoke guidance and grace to them (and us) through the Torah and the Prophets. This God finally entered human events as a person like us, experiencing human life, being obedient to God's Word (which in Jesus' understanding clearly revealed God's intention for human sexual expression), so that in his death there would be a sacrifice for our sins, and then through raising Jesus from the dead validating the claims and teachings of Jesus. These texts announce that through the Messiah, the Christ, we too may live freely by the Word and in the power of the Holy Spirit. If this God is truly God, then the guidance of God's Word (including sexuality) is trust worthy. If the Word (Torah, Prophets, Historical books, Wisdom books, Psalms, Gospels, and the Epistles) are not trustworthy (including sexual guidance), then the God of the Bible is a ruse, a colossal deception!
Now, this is what is at stake in the "analysis" of these texts. Most of the world could care less about these ancient writings, seeing them as irrelevant and too troublesome to bother with. However, the way a person reads these texts determines whether one embraces "the faith delivered to the saints" or instead rejects it for a new designer faith of one's own fancy. The latter leads to temporary peace with this world but is in eternal conflict with God and creation. The former leads to a life of temporary conflict with this world but is at eternal peace with God.