I suspect that John Climacus has Exodus 32 in mind:1
11 But Moses implored the Lord his God and said, “O Lord, why does your wrath burn hot against your people, whom you have brought out of the land of Egypt with great power and with a mighty hand? 12 Why should the Egyptians say, ‘With evil intent did he bring them out, to kill them in the mountains and to consume them from the face of the earth’? Turn from your burning anger and relent from this disaster against your people. 13 Remember Abraham, Isaac, and Israel, your servants, to whom you swore by your own self, and said to them, ‘I will multiply your offspring as the stars of heaven, and all this land that I have promised I will give to your offspring, and they shall inherit it forever.’” 14 And the Lord relented from the disaster that he had spoken of bringing on his people. (ESV)
Moses could be seen here as the "spiritual director" who turns God's wrath away from his "spiritual children." On the other hand, if the Israelites anger Moses, they have no one to stand between themselves and Moses. Thus, it is "better" to anger God, rather than the spiritual director.
Given the way John presents this, it seems doubtful that he would extend this teaching beyond this perhaps tongue-in-cheek usage. He introduces it as something that would sound strange to his audience, and then closes by calling the two sins "the same thing." Thus, his argument seems to be: it's bad to sin against God, and it's bad to sin against your spiritual director, but at least if you sin against God, you have a spiritual director who can plead with God on your behalf.
- For what it is worth, this Eastern Orthodox blogger recommends the same passage with respect this quote.