Jesus doesn't mention it specifically however he does exhort people to avoid sexual immorality. We get the definition of that in the OT including specific prohibition of homosexuality in Leviticus. Jesus quotes the OT including Leviticus meaning that he considers it authoritative. Jesus claims that he did not come to abolish the law but to fulfill. It would be fair to say that he amends it in a few specific circumstances, notably in terms of how sinners are punished. He doesn't actually change the OT definition of sin however. As far as biblical arguments go that's about as good as it gets short of specifically calling something out. The argument that Jesus would've supported homosexual behavior is pretty dishonest to tell you the truth. If someone wants to support homosexual behavior it would be better for them to just say "you know what? Jesus just isn't for me" than to teach falsely about him.
Matthew 15:
19"For out of the heart come evil thoughts--murder, adultery, sexual immorality, theft, false testimony, slander."
"Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them." Matthew 5:17
Jesus even says that he didn't have time to tell his disciples everything
John 16:
12"I have much more to say to you, more than you can now bear.
13But when he, the Spirit of truth, comes, he will guide you into all the truth. He will not speak on his own; he will speak only what he hears, and he will tell you what is yet to come."