(1) Human nature is a complete description of the human such that it applies to every human and not to anything else.
(2) All morality is derived from human nature: Without a belief in human nature, no morality is possible: Every moral law is simply part of human nature.
(3) It is part of human nature that humans have genitals, male or female. The purpose of these genitals is the creation of new life. When they are used in a way such that new life can be created, it is called coitus.
(4) Coitus causes various physical events to occur.
(5) To cause a body to go through the physical events of coitus outside of coitus is contrary to the purpose of those physical events.
(6) To cause physical events of the body contrary to their purpose is contrary to human nature.
(7) What is contrary to human nature should not be done by humans.
(8) Humans should not cause the physical events of coitus outside of coitus.
That is the moral case, and now the legal case:
(9) The conception of children is necessary for the continuation of the human species.
(10) Coitus is the only natural way to conceive children: to conceive children any other way is contrary to human nature.
(7 again) What is contrary to human nature should not be done by humans.
(11) The human species should be continued through coitus.
(12) Coitus should be done only in the context of a commitment to engage exclusively with each other and to support each other and any children conceived. This commitment is called marriage.
(13) The human species should be continued through coitus in the context of marriage.
(14) Society ought to support what should be done for the continuation of the human species.
(15) Society ought to support marriage.
(16) Since two people of the same gender cannot engage in coitus, and therefore cannot cause the continuation of the human species, it is incorrect for two people of the same gender to call themselves married or to claim the support that society owes to marriage.
Notes: I use coitus here in order to be specific about what act I mean. It is defined in #3. #10 is about insemination, in vitro, surrogate parenting, etc. The Church is consistent on this point and opposes any conception of children outside of coitus, even when done by a husband and wife. #6 and #10 are probably the grounds where those who disagree with the conclusions would want to fight, though some would want to fight about #7. I do not claim that #12 is proven. Its proof would be just as long and a distraction from the question at hand. It is only here for definition.
The conclusion in #16 does not mean that they cannot have some other commitment to each other (partnership) or that society cannot support this other commitment with legal protections. However, the legal definition of such a commitment should not require a violation of #8.