The whole idea of "sustaining" office-holders in the church stems from what the D&C calls "common consent." All actions of the church are meant to be governed by this common consent, which means the membership of the church directs the operations of the church, if we're following the scriptural forms. See D&C 26:2 and D&C 28:13. The D&C describes a church where leaders get authority from the consent of the members they'll lead, not by virtue of a priesthood office, and in the early days of the church it wasn't uncommon for members to engage in some discussion as they tried to find someone they could agree on, to fill a vacant office.
Today, on the other hand, members are expected to vote for the leaders they've been assigned, and if you can't do that in good conscience, you lose your temple recommend. In other words, you have to be willing to vote the way the church tells you to vote. This in contrast to the system the scriptures describe, where the church is required to abide by the vote of its members.
The idea of voting for church officers in any situation where the outcome is not necessarily a foregone conclusion may seem somewhat repugnant to modern members, but serves a real and valid purpose. D&C 124:144 specifically allows church members to disapprove people called to offices. In the 1940s the church patriarch was yet another Joseph Fielding Smith (not the famous one, nor his famous abbreviated father). Smith was widely known for predatory homosexuality, as witnessed by his police record full of complaints regarding University of Utah students he had propositioned, or worse. Yet because the church had already become so proficient at stifling dissent, his sustaining as church patriarch was as mutely unanimous as the sustainings we're used to today. It wasn't until a few years later that someone finally got the word to church leadership, and Smith was released for "ill health." (see Smith's wikipedia article, or http://www.connellodonovan.com/smith.html for details). The church called Smith's cousin, Eldred G. Smith, to take the office, which he held until he was given emeritus status in 1979. The office was never refilled, and today no longer exists.
Today, however, we have this strange new idea of sustaining. In October 2014, Elder Nelson went so far as to say this:
Our sustaining of prophets is a personal commitment that we will do our utmost to uphold their prophetic priorities. Our sustaining is an oath-like indication that we recognize their calling as a prophet to be legitimate and binding upon us.The scriptures say nothing of an oath when establishing common consent. Does Elder Nelson mean we promise to do whatever the church's leadership tells us to do? We're not supposed to put faith in mortals, only in Christ; therefore, the church's leadership can mess up just as much as any of the rest of us; we'd best not covenant before God to obey them no matter what.
The temple recommend question on the subject is interesting:
Do you sustain the President of the Church of Jesus Christ of Latter-day Saints as the Prophet, Seer, and Revelator and as the only person on the earth who possesses and is authorized to exercise all priesthood keys? Do you sustain members of the First Presidency and the Quorum of the Twelve Apostles as prophets, seers, and revelators? Do you sustain the other General Authorities and local authorities of the Church?Taking a dictionary definition of "sustain" instead of Elder Nelson's oath definition helps make sense of this question; we can thereby consider that to sustain is to uphold, encourage, support, etc. And it's clear who we're talking about in the first question: the one president of the church. But what does "the Prophet, Seer, and Revelator" mean? "The" is a definite article; is there only supposed to be one? Moses wanted everyone to be prophets, and the scriptures talk about times when there were many. What exactly qualifies someone as a "prophet" is a question worthy of a dissertation, and revelator too, but "seer" is very strictly defined in Mosiah 8:13 as someone who has "wherewith that he can look, and translate all records that are of ancient date". The church hasn't had a translator since Joseph Smith -- no one even claims that ability -- so apparently we don't have a seer. Should President Monson or his successors ever make that claim, I'll certainly take notice, and uphold him in any way I can if it checks out. Certainly he is called to be a seer, but I see no evidence he has fulfilled that calling.
As to priesthood keys, Brigham Young himself tells us the church doesn't have "all priesthood keys," (Journal of Discourses, 15:137) and in case we thought we might ignore Brigham, Pres. Kimball quoted him (General Conference, April 1977), and Elder Oaks recently quoted Pres. Kimball quoting Brigham Young (General Conference, April 2014), all saying there are keys we don't possess, including specifically the key of revelation. Therefore the president of the church is not authorized to exercise all priesthood keys.
But don't bring any of this up, because if you do, you won't get your temple recommend.
I'll gladly support anything the leadership of the church does which indicates they are indeed prophets, seers, or revelators. But they've never demonstrated those fruits, as far as I know, and Christ tells us we should distinguish true prophets from false ones by their fruits (3 Nephi 14:20). Meanwhile, it doesn't take long to come up with a long list of actions taken by church leaders in direct contradiction of scripture. These violations were, I'm confident, not committed maliciously, but they're still non-scriptural, and the leaders involved have refused to correct the problem even when it is called to their attention. I cannot in good conscience support violating scripture, so I can't sustain those actions they have taken.