WHY WE SHOULD INCLUDE SAME-SEX MARRIAGE IN THE UMC:
I don’t find a compelling argument as to why the respective sexes/genders of a couple are consequential for marriage. Scripture, especially when read consistently with other denominational policies (i.e. remarriage), doesn’t settle the issue. Given the explicit commitment to the essential common humanity of men and women by the UMC, no position that rests upon the essential difference between sexes is appropriate.
Yet I haven’t adequately explained why it the UMC should include same-sex marriage. My argument here has been framed by the question of whether or not the UMC should include same-sex marriage as an endorsed and acceptable form of marriage. I find no compelling reasons to not do so, and find most of those offered to be riddled with problems. In fact, in consideration of the Bible and theological implications for stating otherwise, I find no reason that a particular pairing of the sexes/genders of a covenanting couple is essential to the definition of marriage.
This issue comes down to determining what marriage is really about. What is its purpose? The Bible, from my view, tends toward the direction of claiming its purpose is procreation. However the case isn’t simple, as it’s also shown to be used for political and social reasons. What do we think about this? Is the purpose of marriage to procreate? This idea is found nowhere in any UMC discipline or liturgy. In fact, the Book of Discipline is intentional to include the note that marriages with or without children are seen equally in the eyes of God. Establishing procreation as the purpose for marriage would, among other things, require an ecclesial prevention of heterosexual marriages between people who are knowingly unable to procreate, obviously including those who have medical/biological reasons, including being post-menopausal.
The most robust description of marriage in the UMC can be found in the Book of Discipline: a “covenant that is expressed in love, mutual support, personal commitment, and shared fidelity.”  If indeed this is the purpose of marriage, and I affirm it as such, then no particular pairing of sexes is necessary to it. I understand marriage in principle, and the UMC seems to understand it in practice, to be a uniquely lifelong dedicated commitment of companionship, relational proximity, and love, from which the love of God is made known. And there is no reason that such a purpose cannot be realized by a couple regardless of their gender/sex pairing. What matters is the commitment and practice of unity and fidelity.
It must also be recognized that continuing to prohibit such marriages is a refusal to recognize the full humanity of our LGBT sisters and brothers, which can be seen clearly in the experiences of those who are most directly affected by such prohibitive policies. Given these things, the final consideration for whether or not the UMC should fully include same-sex marriage is a consequentialist one: what might be the consequence of being in a same-sex marriage for the life of a follower of Jesus? While this question may seem paternalistic it cannot be overlooked. If indeed a particular practice was deemed destructive or dangerous to the life of an individual, it ought not be approved by the church.
Per the first concern above, about how prohibitive policies affect others, we need to embrace the fact that the Wesleyan tradition places value upon lived experience.  For this issue we must listen to the voices of those most affected by policies like our current one. For the sake of space I’ll provide only one example. This is from James Alison, not a United Methodist but one directly affected by prohibitive policies such as ours in his own tradition:
Consider what the current teaching…is: ‘The homosexual inclination, though not itself a sin, constitutes a tendency towards behaviour that is intrinsically evil, and therefore must be considered objectively disordered.’…
This is interposing itself between the regard of Christ and our own sense of being, in a way which tends to pervert the simple regard of one who loves us as we are, and as loved we will find ourselves becoming someone different. It is teaching us instead that God will only love us if we start from somewhere else… 
Per the second concern above, a Wesleyan way of phrasing the consequentialist question might be: would it help or hurt in the process of becoming more loving of God and neighbor? Therefore the question in front of us is something like, does entering into the covenant of same-sex marriage necessarily diminish or preclude one’s ability or capacity to love God and neighbor? Or could it encourage and contribute to one’s ability or capacity to do so? There is nothing intrinsic to marriage (heterosexual or not) that necessarily answers either of these questions affirmatively, even though a healthy marriage does so to the latter. I see no reason to think that same-sex marriage is any different on these questions than heterosexual marriage. I see no reason to think that same-sex marriage necessarily diminishes or precludes one’s ability or capacity to be/become Christ-like.
For all of the reasons here it seems to me that the church should drop any particular gender/sex pairing as intrinsic to the definition of marriage and therefore perform, and ordain those within, same-sex marriages in exactly the same way and for exactly the same reasons the church already performs and ordains those within heterosexual marriages. The UMC should therefore marry any couple, regardless of their sex/gender pairing, that commits to entering into a relationship of mutual love, fidelity, and longevity.
 The Book of Discipline of the United Methodist Church, ¶161B (109).
 See, among others, Donald A.D. Thorsen, “Experimental Method in the Practical Theology of John Wesley,” Wesleyan Theological Journal 24 (1989).
 James Alison, On Being Liked (London: The Crossroad Publishing Company, 2003) 102-103 (sic).