Homosexual logic is the "logic" used to justify the Homosexual Agenda. Like liberal logic generally, homosexual logic relies on statements that appear to be logical but that are actually rife with logical fallacies. Examples include:

Calling things the opposite of what they are, e.g., justifying their special rights as just another form of equal protection.
Improperly shifting the burden of proof by asserting that homosexuality must be understood as not a choice until it is conclusively shown to be one.
Slippery slope arguments in which they argue that repression of homosexuality will lead to a series of bad results that actually will not follow or that have nothing to do with homosexuality.
Cherry-picking only those parts of the Bible that suit their purposes, while arguing that any parts of Scripture that are inconvenient to them need to be "interpreted" correctly or were "nailed to the Cross," or that just by mentioning them, you are "twisting" them in some unspecified way.
Taking it for granted that any book with a pro-homosexual slant must be true, rather than critically assessing whether that book is credible.
Appealing to majority will, but only when it suits them; switching back and forth between "This is what the people want" and "America is a republic, not a democracy."
Demanding that their own interpretation (or misinterpretation) of the Bible be made binding on everyone, despite the establishment clause.
Demanding limited government, but only when it suits them, while supporting government oppression of anyone they don't like.
Claiming to be persecuted when in reality it is they who are doing the persecuting.