My opponent didn't give much of a defense nor did they do a great work with citing so I will do my best to respond with what they presented.
First we need to understand why Jesus came. He came to give us a new law. The older laws against homosexual relations are gone. Jesus redeemed us from the curse of the law. By the works of the law no person will become justified. All that matters now is love, and same-sex couples certainly have love.
My opponent seems confused on what the Bible actually teaches. They are correct in that Christ came to give us the New Law (aka Law of the Gospels), however, my opponent posits that this would then abrogate the entirety of the law prior, or maybe just for homosexuality (?). Yet Christ Himself says, "Do not think that I have come to abolish the law or the prophets. I have come not to abolish but to fulfill"(Mt. 5:17). It is also possible my opponent doesn't understand the different types of laws; i.e. civic, ceremonial, moral. Because my opponent isn't very clear by what they mean I cannot firmly argue against them. My opponent goes on to make various claims without textual nor theological support, i.e. justification, same-sex couples have love, etc. Again, due to a lack of explanation I cannot properly argue against the terms used. It should be noted that my opponent does posit that the OT (Old Testament) does ban homosexual relations.
Jesus is the way, the truth. Anyone not with Jesus is against him. He never mentioned homosexuality. Imposing a ban on homosexual acts is not the truth or way to eternal life.
Here my opponent makes a fallacy (argumentum ex silentio) and a contradictory statement. First, Christ not mentioning homosexuality does not ergo mean homosexuality is no longer a sin. Second, my opponent then says that imposing a ban on homosexuality is not the truth or way to eternal life. Following my opponent's own position, Christ having never mentioned homosexuality, my opponent cannot say that it would be contrary to Him as He never mentioned the subject. Unless my opponent is going to cite where He promoted or lifted the ban, this whole statement was erroneous and illogical.
Although Christ doesn't mention the term homosexuality, He does mention what a proper sexual union looks like in Matthew 19:4-6, "'Have you not read that from the beginning the Creator ‘made them male and female’ and said, ‘For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh’? So, they are no longer two, but one flesh. Therefore, what God has joined together, no human being must separate.'"
The bible also forbids acting against your nature. So, one of the verses used against gay sex is in Romans 1. But the verse actually forbids acting against your own nature. Gays were made gay, so forbidding them to act gay is not following Paul. Paul himself said "all things are lawful." Paul said we were free. Paul was clearly ok with it.
Because my opponent only made a general reference to Romans 1, I will assume that all that was mentioned in this paragraph is in reference to said book and chapter. Let's look at the passage in question:
Romans 1:26-27 Therefore, God handed them over to degrading passions. Their females exchanged natural relations for unnatural, and the males likewise gave up natural relations with females and burned with lust for one another. Males did shameful things with males and thus received in their own persons the due penalty for their perversity.
My opponent claimed that the verse forbids acting against your own nature. They are correct but not in the sense that they posit. What is natural is male-female relations. This is shown in God's creation of Adam and Eve and the command to "be fertile and multiply" (Gen. 1:26-28). In the verse my opponent referenced, it states that the natural relations given up by the males were with females and is in reference to the females mentioned prior exchanging the natural for the unnatural (note the word "likewise" denoting a similar action). If we are to take the text for what it says, then what is natural is the heterosexual relationship and the unnatural the homosexual relationship.
My opponent made another astonishing claim, without citations of course, that Paul said, "all things are lawful", and was thus okay with homosexual relations. This is nowhere in Romans 1; however, we do find Paul stating this in 1 Cor. 6:12 "'Everything is lawful for me,' but not everything is beneficial. 'Everything is lawful for me,' but I will not let myself be dominated by anything", and 1 Cor. 10:23 "'Everything is lawful,' but not everything is beneficial. 'Everything is lawful,' but not everything builds up." Paul is actually speaking against these "slogans of liberty" in the passages. Liberty is not merely doing whatever you want and whatever is beneficial to you, but rather doing what is right and just. Hence, Christians will state that sin is slavery (John 8:34) and acceptance of God's grace and fulfilling His commands is freedom.
Let's not forget, prior to the first use of the slogan in 1 Cor. 6:9-10, the same Paul says, " Do you not know that the unjust will not inherit the kingdom of God? Do not be deceived; neither fornicators nor idolaters nor adulterers nor homosexuals nor thieves nor the greedy nor drunkards nor slanderers nor robbers will inherit the kingdom of God." My opponent will be quick to point out that in the translation I have cited (NASB) the word "homosexuals" isn't there in the Greek. They would be right. The two Greek words that were combined in this translation were malakoi (μαλακοὶ) and arsenokoitai (ἀρσενοκοῖται). Fun fact, Paul actually coined the latter term himself, prior to being written it didn't exist as far as scholars are concerned. These have such a wonderful array of translations available; malakoi can be translated as boy/male prostitutes, submissive/effeminate males in a homosexual relationship and arsenokoitai can be translated as homosexual, sodomite, dominant male in homosexual relationship. It seems Paul explicitly does not feel the same way about homosexuality as my opponent claims.