Here is a common argument for gay marriage that I have heard multiple times.

[1] Justice requires that all people be treated equally by the state.
[2] Homosexuals are people.
[3] The marriage act does not treat homosexuals
equally to heterosexuals unless it is amended to allow for Gay marriage,

Therefore

[4] Justice requires that the marriage act should be amended to allow for Gay
marriage.

This argument is formally valid. If its premises are true, the conclusion follows. However, with the exception of premise [2] every premise is false which means it is unsound.

Re [1] It is not true that justice requires that the state treat all people equally. Consider a person guilty of a crime. A person guilty of a crime is a person yet clearly justice does not require that the state treat the guilty the same way it treats the innocent. Criminals are deprived of their liberty rights (they are incarcerated), their property rights (fined) or in some cases their life (capital punishment) those who do not engage in crimes are not deprived of these things.

I am not trying to say that gay people are on par with criminals, I am making the point that the state does not in fact treat all people equally.

Further, justice does not require that all people be treated equally. The classical definition of justice is to "render to each what is his due." As Wolterstorff notes in God, Justice and Duty:

[In some contexts] that which is due to them is some ‘evil’ in the other cases ... that which is due them is some life-good. If it is a life-good that is due them, then what is
due them is what they have a right to, what they are entitled to. If it is an "evil," what is due them is their desert.

To make the case, the defender of homosexual marriage needs to supplement [1] with two further arguments (i) that those who engage in homosexual relationships have not done anything wrong which would deserve them being treated differently; and, (ii) a state sanctioned marriage is a right. Simply, citing dubious claims about equality does neither.

I don’t think either claim is plausible: regarding (i), it is seriously immoral to have sex with a member of the same sex, consequently a person who enters into a Gay marriage is in fact taking a vow expressing commitment to a life of immoral activity.

Re (ii), the state’s function is to defend the innocent against aggression and to punish those who commit crimes. Performing marriage ceremonies constitutes neither.

Re [3] the marriage act does not treat homosexual persons differently to heterosexual persons. Under the marriage act a heterosexual person can: (a) enter into a informal marriage (de facto) with any number of people of either sex providing it is consensual and the person is not a close relative, (b) have a private ceremony to recognise, celebrate or solemnise any such marriage, (c) have the state solemnise and recognise a formal marriage with one member of the opposition sex provided it is consensual and not with a close relative.

Similarly a homosexual person can (a) enter into a informal marriage (de facto) with any number of people of either sex providing it is consensual and the person is not a close relative, (b) have a private ceremony to recognise, celebrate or solemnise any such marriage, (c) have the state solemnise and recognise a formal marriage with one member of the opposition sex provided it is consensual and not with a close relative.

So the marriage act grants identical rights to homosexuals and heterosexual persons. What the act does is discriminate against certain sexual relationships. However, the principle expounded in [1] is that all people should be treated equally, not, that all sexual relationships should be treated equally.

Again, it seems the defender of this argument needs to say more, he or she needs to maintain not only that justice requires that all people be treated equally but also that all sexual relationships should be treated equally. But this is clearly absurd, it entails that the state should treat the case of Miewes and Brandes the same as it treats a married couple who consummate their wedding.

Finally, even if [3] were true and the marriage act does not treat homosexual persons equally to heterosexual persons it would not follow that it does so unless it is amended to allow for Gay marriage. An obvious way equality could be restored would be for the state to recognise no marriages. A proposal some libertarians have put forward and one we support too.

So as far as I can tell this argument is worthless and certainly is unsound. Of course, this will not stop defenders of gay marriage trotting this argument out ad nauseum. Providing credible arguments for their position has never been a forte.