The idea that Christ's presence is indefectible from the church is a comforting counterpoint to implications from claims of infallibility or inerrancy. It is not that the church is made up of superior beings of some sort, but that
if we are faithless,
he [Christ] will remain faithful,
for he cannot disown himself.
II Timothy 2:13
The church, the gathering of people faithful to Christ, is his strange choice of a body to preach his message and minister his "means of grace," as the Book of Common Prayer puts it in the General Thanksgiving.
It is historically and anecdotally obvious that the church finds many ways to be faithless, to "defect" from Christ's authority and purpose. It is filled with entirely defective individuals, whose "membership" will not keep them out of hell:
Matthew 13:24 He put before them another parable: "The kingdom of heaven may be compared to someone who sowed good seed in his field; but while everybody was asleep, an enemy came and sowed weeds among the wheat, and then went away. So when the plants came up and bore grain, then the weeds appeared as well. And the slaves of the householder came and said to him, 'Master, did you not sow good seed in your field? Where, then, did these weeds come from?' He answered, 'An enemy has done this.' The slaves said to him, 'Then do you want us to go and gather them?' But he replied, 'No; for in gathering the weeds you would uproot the wheat along with them. Let both of them grow together until the harvest; and at harvest time I will tell the reapers, Collect the weeds first and bind them in bundles to be burned, but gather the wheat into my barn.' " Matthew 13:24-30
I am in a middle stage of earthly life in which almost every personal defection seems to have a spotlight on it. I seriously wonder if I am a weed planted amidst wheat. And the frustration I experience with myself makes me more harsh about other folks' defections.
The idea of indefectibility challenges that grim point of view with the exaltation of Christ alone. It is Christ who is without defect and is never a defector. As one hymn expresses it,
The soul that on Jesus has leaned for repose,
I will not, I will not desert to its foes;
That soul, though all hell should endeavor to shake,
I’ll never, no never, no never forsake.
Feelin' defective this season, Lord. My soul's feeling shaken, big time. A little sign that I'm in on your indefectibility, please?