(1)Though Paul mentions it twice, Jesus does not talk about homosexuality at all in the Gospels that we have as canon.(2) An argument from absence isn’t necessarily very compelling, but it is worth mentioning that for over 30 years we have energetically argued over something that the authors of the Gospels did not feel was worth mentioning even once one way or another.(3) Paul, the first to write about Jesus whose manuscripts we have, encouraged people not to marry at all because he expected the imminent return of Jesus in his lifetime.(4) He did not speak of committed LGBTQ relationships any more than the Hebrew scriptures did.(5)
1. It is possible, when trying to shoe-horn homosexuality into Jesus' concerns is to mention his use of the word aselgeia in Mark 7:22, and that this word possibly may have referred to homosexuality - or any number of sexual sins. The fact is that no translator, all of whom were quite willing to show an anti-homosexual bias in translating toevah as 'abomination' in the OT only where it apparently referred to same-sex acts, saw fit to translate any word of Jesus in the gospels as referring to homosexuality. In mistaken etymological inventions like the term "sodomy", we see clearly that they were inclined to do so if the opportunity presented itself. It is also the case that only Tom Hobson and one other Biblical itnerpreter he is aware of would even make this argument. So of all the Biblical interpreters he might be aware of, only 2, one of which being himself, would argue that Jesus mentions homosexuality at all.
2. And in 1 Corinthians and 1 Timothy, Paul only makes mention of 'coitus' between two males, not mentioning 'coitus' between females at all. Why is this? This mistake on his part precludes support for complementarianism. Perhaps it is similar to his concern with 'effeminate' men in both of these passages? (Using a Greek word that can be taken to mean more broadly 'soft' - again, translator's bias, in this case, misogynistic bias). Should we take the fullness of this list of 'sins' and begin booting men who wear pink shirts from the pews? In short, no.
3. So silent is Jesus on the matter that no translation we are aware of uses the word homosexual, or a derivative thereof, anywhere in the four Gospels. But, again, an argument from silence is not a powerful argument. Jesus is also silent on solar energy and embryonic stem cell research - that doesn't mean the gospel implies nothing about these things. In fact, the Gospel implies that justice and inclusion are part of God's plan for salvation, especially inclusion of groups that the religious establishment looks down upon and views as 'unclean'.
4. As we have mentioned before, for Paul, marriage was at best a grudging allowance for those who simply could not remain abstinent until Christ's return. As for Christ, he clearly demonstrates that even "family" far exceeds the traditional roles, being not about blood, but about living out one's faith.
5. His focus, like that of many opponents of justice for LGBTQ persons, is on the particular sex acts themselves, almost exclusively a focus on sex acts shared between two males. One could account for this myopia entirely with reference to the well-established connection between homophobia and misogyny. The concern is that a man defiles, or demeans himself, in behaving like a woman and having sex with a man. Women are not mentioned in this misogynistic construct because feminine honor is of far less concern. It is possible that none of this is really about sex at all, but about sexism - homophobia's Siamese twin.