All of us are in ministry by virtue of our baptism, not our ordination -- says the official UM literature. I would agree. All of us are kings and priests to Almighty God through Jesus Christ. Now, come my Catholic friends (Anglo-, Roman, Old, whatever), saying, "But you don't have a sacerdotal priesthood. Your understanding of ministry is all different from ours." But I don't think we're as different as all that.
We really do believe in priesthood -- the Priesthood of All Believers. After all, there's nothing magic about my hands, that I can baptize or offer eucharist where someone else can't. Oh, but some will say that there is an ontological something-or-other conferred in ordination that changes this. But even among Catholics (Anglo-, Roman, Old, whatever), emergency baptism by laypersons is allowed. So there can't be anything conferred in ordination that enables one person's baptizing to be effective, and condemns another's to be ineffective. All believers have the same raw ability to exercise the power of God.
The difference between laity and clergy is one of authority. I have the authority to baptize and offer eucharist. This authority is given me by the Church, which can take it away if I am disobedient. When others submit to my authority to offer on their behalf, instead of trying to do it themselves, they please God and build up the Church. When I use my authority in service to them (rather than to please myself), I please God and build up the Church.
Now, if all believers have the same raw ability to exercise the power of God -- including baptizing and offering eucharist -- then women as well as men must have that same raw ability. The question is then one of authority. Can the Church give them the authority to act on behalf of the Church? My Catholic friends (Anglo-, Roman, Old, whatever), as well as my Orthodox friends, would say, No. They say that God has revealed the pattern of the all-male priesthood (sacerdotal ministry): implicitly in Scripture, explicitly in Tradition.
In Scripture, we see a lot of examples of the dog-that-didn't-bark variety: no women were appointed to leadership by Christ or the Apostles. Yeah, well, women weren't doing a lot of things in those days. To say that they should be barred forever from things they used to not be eligible for is an odd thought.
Then there's Paul, saying that women shouldn't be teachers, or exercise authority over men. That's a far more powerful argument. But most of those who make much of it are happy that women should exercise other forms of teaching and authority. And I wonder what my Catholic friends (Anglo-, Roman, Old, whatever) make of people like Hilda, Abbess of Whitby. There were many very strong female leaders in the ancient, undivided Church. They weren't priests, but they did exercise authority over men, for they presided over "co-ed" monastic establishments.
And if women need a "covering," as my charismatic friends put it, is not the whole governance of the Church "covering" enough? All of us are answerable for our lives and teaching to somebody; nobody gets a pass. At least in our UM church governance, even bishops have accountability structures. I don't see that we do violence to Scripture to allow for both sexes to do jobs that used to be reserved for just one.
As for Tradition -- which should (and does) mean more than "what we've always been comfortable with" -- there have always been significant transition points where the Church has endorsed new ideas. As the Council of Jerusalem put it, "it has seemed good to the Holy Spirit and to us." So I Nicea, after much debate, used a non-scriptural word to define the relationship of the eternal Son to the Father (homoousios). Other decisions have been made along the way -- never too many, since continuity and clarity matter. The Spirit doesn't change his mind every whipstitch. But surely a Church can say (assuming that Scripture isn't just up and stood on its head), "it seemed good to the Holy Spirit and to us" to grant the authority that flows from ordination to those women who can demonstrate the proper call and fitness for the role (just like men). Likewise, if a Church remains unconvinced of the Spirit leading them in that direction, it can refuse to do so.
This is not intended to be a criticism of any other Church's way of doing things. Who am I to judge the rules of an organization I don't belong to? So I'm not making pejorative references to anybody else. Let them do as seems right to them. But I am happy to be in ministry with many orthodox and faithful sisters in the clergy.
Meanwhile, the contest over orthodoxy within the clergy of all the major denominations goes on. One of the major irritants is the ideology we call feminism, especially "radical" feminism, which tends to see male/masculine/patriarchal as negatives and offers a view of humanity that seems to me to be skewed toward a kind of genderized Marxism. Such a view I find incompatible with Christian thinking. But not all the radical feminists out there are women. It's the ideas that are pernicious, not people.