After discussing this with our rector, I discovered that the key bone of contention is Section 4, the enforcement mechanism (or lack thereof) that holds the Anglican Communion together.
The subtext of disagreement, of course, is the subject of the authority of the Scripture in Anglican life. Probably the most visible manifestation of this debate is the question over same-sex blessings and the elevation of homosexuals to the priesthood, and in 1 1/2 cases, the office of bishop. (One = Gene Robinson in New Hampshire, 1/2 = the process for replacing the Bishop of Los Angeles in which three of the six candidates were publically acknowledging and celebrating their own homosexuality.) Support for this is strongest in the West, particularly in Canada and the United States. In contrast, most of the growth in the 80 million member Anglican Communion is in Africa, where attitudes are quite different.
The question on the table for the Anglican Communion is how such a wide diversity of opinion can co-exist. If a bishop is elevated who, at least in the minds of one wing, is living in open and unrepented sin, the Biblical mandate is fairly clear - that person should be excommunicated. By contrast, the Anglican Covenant requires the following procedure:
(4.2.4) Where a shared mind has not been reached the matter shall be referred to the Standing
Committee. The Standing Committee shall make every effort to facilitate agreement, and may
take advice from such bodies as it deems appropriate to determine a view on the nature of the
matter at question and those relational consequences which may result. Where appropriate,
the Standing Committee shall refer the question to both the Anglican Consultative Council
and the Primates’ Meeting for advice.
(4.2.5) The Standing Committee may request a Church to defer a controversial action. If a
Church declines to defer such action, the Standing Committee may recommend to any
Instrument of Communion relational consequences which may specify a provisional
limitation of participation in, or suspension from, that Instrument until the completion of the
process set out below
This is bascially the status quo - The ABC asks everybody not to provoke anybody in either direction. The problem for conservatives is that acquiesence is tacit to complicity. "Woe to those who call evil good and good evil," would be their response.
The Economist (3/24/12) describes the situation this way:
In the 80m-strong worldwide Anglican Communion, things are even messier. American liberals hate a covenant which Anglican churches are being asked to sign, pledging to avoid provocative actions like consecrating openly gay bishops. If the future Archbishop of Canterbury insists on the covenant, bits of the communion may reject the arrangement whereby an English prelate chairs the global fraternity, says Frank Kirkpatrick, an American Episcopalian priest. An emerging block of African and American conservatives also questions Canterbury’s historic role. For some hardliners, the covenant does not go far enough in penalising liberals.
The next Archbishop of Canterbury will also have to answer a more basic question: is the institution he heads part of the establishment, with an accepted role as its moral guide, or is it called on to be a provocateur, speaking its own version of truth to power? Defeat over gay marriage will make it tougher to play the first role, but a church that strives to be idiosyncratically prophetic will be harder to keep together. And the church’s role at home has implications for the communion: can an English church that is steadily disestablishing itself retain any natural place as a pacesetter for much bigger churches abroad?
In short, Canterbury is in a no-win situation, and it is not clear if anyone (let alone the likely nominee John Sentamu) could hold it together. The covenant appears to be a weak attempt at reconciliation without any teeth.