Are Same Sex Unions Marriage?

A question commonly asked is; do you believe same sex couples should be allowed to marry? It seems to me the question assumes an answer to a question that hasn't been proven yet. Most who ask this question are begging an affirmative answer to the question, can same sex couples marry? When I was a child and asked my coach for permission to run the mile, my coach and I accepted as fact that I was able to run a mile. A 'May I' question presupposes the 'Can I' question has already been answered to the affirmative. When I hear the question, do you believe same sex couples should be allowed to marry, it hits my brain the same as asking should a quadriplegic be allowed to run the mile. I would say no, but someone could make the case that they can move by artificial means so therefore they can run the mile. But have they just changed the definition of 'run?'  It seems to me that marriage is something specific as opposed to anything. Just as 'run' means something specific as opposed to whatever civil law decides it should be. If a word, like run, can mean anything than really it's meaningless; (I'm going for a run to the run for about run and get run, run my run.) Is marriage something or nothing? Is it found in natural law as part of the nature of man or is it anything/nothing? Thomas Aquinas reasoned in the 13th century that marriage is something found in natural law. In his reasoning, he refers to Ulpian of the third century, Cicero of the first century BC, and Aristotle of the fourth century BC. The bolded is from Aqinuas:

Article 1. Whether matrimony is of natural law? 
Objection 1. It would seem that matrimony is not natural. Because "the natural law is what nature has taught all animals" [Digest of Justinian I, i, de justitia et jure, 1.] But in other animals the sexes are united without matrimony. Therefore matrimony is not of natural law. 
Objection 2. Further, that which is of natural law is found in all men with regard to their every state. But matrimony was not in every state of man, for as Tully (Cicero) says (De Inventione. I,ii), "at the beginning men were savages and then no man knew his own children, nor was he bound by any marriage tie," wherein matrimony consists. Therefore it is not natural. 
Objection 3. Further, natural things are the same among all. But matrimony is not in the same way among all, since its practice varies according to the various laws. Therefore it is not natural. 
Objection 4. Further, those things without which the intention of nature can be maintained would seem not to be natural. But nature intends the preservation of the species by generation which is possible without matrimony, as in the case of fornicators. Therefore matrimony is not natural. 

On the contrary, At the commencement of the Digests it is stated: "The union of male and female, which we call matrimony, is of natural law." 

Further, the Philosopher (Aristotle-Ethic. Book viii, 12) says that "man is an animal more inclined by nature to connubial than political society." But "man is naturally a political and gregarious animal," as the same author asserts (Polit. i, 2). Therefore he is naturally inclined to connubial union, and thus the conjugal union or matrimony is natural. I answer that, A thing is said to be natural in two ways. First, as resulting of necessity from the principles of nature; thus upward movement is natural to fire. In this way matrimony is not natural, nor are any of those things that come to pass at the intervention or motion of the free-will. Secondly, that is said to be natural to which nature inclines although it comes to pass through the intervention of the free-will; thus acts of virtue and the virtues themselves are called natural; and in this way matrimony is natural, because natural reason inclines thereto in two ways. First, in relation to the principal end (purpose) of matrimony, namely the good of the offspring. For nature intends not only the begetting of offspring, but also its education and development until it reach the perfect state of man as man, and that is the state of virtue. Hence, according to the Philosopher (Ethic. viii, 12), we derive three things from our parents, namely "existence," "nourishment," and "education." Now a child cannot be brought up and instructed unless it have certain and definite parents, and this would not be the case unless there were a tie between the man and a definite woman and it is in this that matrimony consists. Secondly, in relation to the secondary end of matrimony, which is the mutual services which married persons render one another in household matters. For just as natural reason dictates that men should live together, since one is not self-sufficient in all things concerning life, for which reason man is described as being naturally inclined to political society, so too among those works that are necessary for human life some are becoming to men, others to women. Wherefore nature inculcates that society of man and woman which consists in matrimony. These two reasons are given by the Philosopher (Ethic. viii, 12).

Reply to Objection 1. Man's nature inclines to a thing in two ways. In one way, because that thing is becoming to the generic nature, and this is common to all animals; in another way because it is becoming to the nature of the difference, whereby the human species in so far as it is rational overflows the genus; such is an act of prudence or temperance. And just as the generic nature, though one in all animals, yet is not in all in the same way, so neither does it incline in the same way in all, but in a way befitting each one. Accordingly man's nature inclines to matrimony on the part of the difference, as regards the second reason given above; wherefore the Philosopher (Ethic. viii, 12; Polit. i) gives this reason in men over other animals; but as regards the first reason it inclines on the part of the genus; wherefore he says that the begetting of offspring is common to all animals. Yet nature does not incline thereto in the same way in all animals; since there are animals whose offspring are able to seek food immediately after birth, or are sufficiently fed by their mother; and in these there is no tie between male and female; whereas in those whose offspring needs the support of both parents, although for a short time, there is a certain tie, as may be seen in certain birds. In man, however, since the child needs the parents' care for a long time, there is a very great tie between male and female, to which tie even the generic nature inclines. 
Reply to Objection 2. The assertion of Tully may be true of some particular nation, provided we understand it as referring to the proximate beginning of that nation when it became a nation distinct from others; for that to which natural reason inclines is not realized in all things, and this statement is not universally true, since Holy Writ states that there has been matrimony from the beginning of the human race. 
Reply to Objection 3. According to the Philosopher (Ethic. vii) "human nature is not unchangeable as the Divine nature is." Hence things that are of natural law vary according to the various states and conditions of men; although those which naturally pertain to things Divine nowise vary. 
Reply to Objection 4. Nature intends not only being in the offspring, but also perfect being, for which matrimony is necessary, as shown above.

It seems clear that Aquinas has reasoned marriage to be something that same sex couples are not able to engage in. So asking that they be allowed to do something they can't isn't rational. Also I've heard the argument that sterile couples, like same sex couples, can still marry. Being unable to function in a specific case does not change the principle end in the general case. For example a man having eyes that do not function (blindness) does not change the principle end of the eye in general. A sterile couple may be broken but they are still married. To claim a same sex union is marriage due to an exception, would be the like claiming my finger is an eye because it can see as well as a broken eye; eye would then be meaningless.

As a final thought, I have not heard an argument for same sex unions to be included as marriage which can stand up to the reasoning that Aquinas as giving to marriage which excludes same sex unions. 

Aquinas' References: 
Natural law is that which all animals have been taught by nature ; this law is not peculiar to the human species, it is common to all animals which are produced on land or sea, and to fowls of the air as well. (Ulpian, Digest of Justinian, Book I.3) 

For there was a time when men wandered at random over the fields, after the fashion of beasts, and supported life on the food of beasts; nor did they do anything by means of the reasoning powers of the mind; but almost everything by bodily strength. No attention was as yet paid to any considerations of the religious reverence due to the gods, or of the duties which are owed to mankind: no one had ever seen any legitimate marriages, no one had beheld any children whose parentage was indubitable; nor had any one any idea what great advantage there might be in a system of equal law.(Cicero, De Inventione, Book I, II) 

From it [natural law] comes the union of man and woman called by us matrimony, and therewith the procreation and rearing of children ; we find in fact that animals in general, the very wild beasts, are marked by acquaintance with this law. (Ulpian, Digest of Justinian, Book I.3) 

Between Husband and Wife there is thought to be Friendship by a law of nature: man being by nature disposed to pair, more than to associate in Communities: in proportion as the family is prior in order of time and more absolutely necessary than the Community. And procreation is more common to him with other animals; all the other animals have Communion thus far, but human creatures cohabit not merely for the sake of procreation but also with a view to life in general: because in this connection the works are immediately divided, and some belong to the man, others to the woman: thus they help one the other, putting what is peculiar to each into the common stock. (Aristotle, Ethic, Book VIII, XII) 
He who thus considers things in their first growth and origin, whether a state or anything else, will obtain the clearest view of them. In the first place there must be a union of those who cannot exist without each other; namely, of male and female, that the race may continue (and this is a union which is formed, not of deliberate purpose, but because, in common with other animals and with plants, mankind have a natural desire to leave behind them an image of themselves), and of natural ruler and subject, that both may be preserved. (Aristotle, Politic, Book I, II) 

The friendship of children to parents, and of men to gods, is a relation to them as to something good and superior; for they have conferred the greatest benefits, since they are the causes of their being and of their nourishment, and of their education from their birth; (Aristotle, Ethic, Book VIII, XII) 

This is why God always enjoys a single and simple pleasure; for there is not only an activity of movement but an activity of immobility, and pleasure is found more in rest than in movement. But 'change in all things is sweet', as the poet says, because of some vice; for as it is the vicious man that is changeable, so the nature that needs change is vicious; for it is not simple nor good. (Aristotle, Ethics, Book VII, XIV)