Probably the main one is that many churchmen have become convinced that homosexuality is established at birth by the genes, etc. Some would include early enviromental influences, too. In any case, this means that some men and women have a natural same-sex attraction, something innate, beyond their control. This is part of their very nature. Some would even say that this must be God-given. In any case, if this is the way certain people are born it is essentially Christian to treat them equally, which means freedom to marry, etc.
(I do not agree with calling it marriage, but have reached the point of approving of civil unions.)
There also is the related argument that this is a matter of equal rights, just as legislation regarding African-Americans was. Many believe that in 50 years we will look back and see the gay movement for equality as justified as that of African-Americans..
How critical should Catholics be of all this when the Church has had such a homosexual mess among its own clergy, leading to serious predatory activity aimed mainly at teenage boys? In fact, one Catholic I know - well-informed - thinks that probably a third of the priests are gay, that gays are attracted to the priesthood for several reasons, among them: (1) a desire to escape this temptation by pledging to be celibate; (2) ordination keeps relatives and others from asking when you will get married; (3) a cover for homosexuality; (4) the attraction of an all-male fraternity; and (5) the aesthetics of the mass, the vestments, etc.
Some Protestants also would argue two other points:
Jesus never mentioned homosexuality.
Yes, homosexual activity is sharply condemned in scripture. In fact, gays were to be stoned to death (Lev. 20:13). Do we really advocate that? Others to be killed include witches, rebellious sons, any woman who marries and is found not to be a virgin, and anyone who worships a God other than Jehovah (Ex. 22:20). Fathers can even sell their daughters into slavery, too.
In a word, if we get literal about the Bible and homosexuality - wow! lots of men and women out that should be put to death.
Now, would Christ approve of that, when the core of his message was to love one another. He also warned us to beware of judging, and he had this habit of hanging out with such outcasts of society as Samaritans, prostitutes and tax collectors.
I disgree with the churches who support gay marriage, but I understand their deep desire to demonstrate the love of Christ - and I respect it.