Using the fact that Jesus pointed to the example of a woman and a man to talk about marriage as evidence that hetero marriages are the only ones he approves of is akin to my former church maintaining that using musical instruments for worship is sinful because the bible only mentions singing and praising with the voice. Of course, not everything not explicitly mentioned is morally permissible, but we have reasonable, common sense to use as a judge. What isn't explicit, we can judge by the two greatest commandments, love God and love your neighbor. When we are doing harm to another, there is room to judge that. Homosexuality, especially a loving marriage between two men or two women, does no harm and brings more love into the world.
You can hardly pull old testament passages forward into time to claim homosexuality is wrong now because the Jews were given laws about it. They were given laws about a lot of "abominations" that no Christian recognizes as needing to be followed. If you want to use that metric, there are a lot of other Levitical edicts you'll have to start following as well.
The only places "homosexuality" is mentioned in the new testament are not by Jesus, and they aren't very solid as far as translation goes. A scholarly reading of the passages to determine the intended meaning of malakos and arsenokoitai - the Greek words translated in some English Bibles as homosexual, effeminate, or sodomite - tells you that "malakos" refers to the pre-pubescent slave boys kept by many wealthy Greek men as prostitutes or sex slaves, and "arsenokoitai" meaning the men who kept those boys. This is made clear by the grouping and structure of the words in the passage. The condemnations come in groups of related sins, like "murderers of fathers, murderers of mothers, and manslayers," "lawless and disobedient," and "liars and perjurers." The group of sins including what is commonly understood as a blanket condemnation of all homosexuality is grouped as, "pornoi, asenokoitai, and andropodistai." Pornoi translates as whoremonger, and andropodistai as slave-keeper or slave-trader. It only makes structural sense that andropdistai is a condemnation of those (literally translated "man-bedders") who bedded the slaves they traded and the prostitutes condemned in the word previous. All three of which were common in the place and time where Paul was writing to Christian churches. A blanket condemnation of homosexuality is not supported by an intelligent translation and is only there because of pre-held bias against it.