The steel-Vulcan in the original quote admits that humans have an edge in the field of interpersonal relations. I imagine that's why the Vulcans let the humans lead; because the humans are capable of persuading all the other races in the Federation to go along with this whole 'federation' idea, and leave the Vulcans more-or-less alone as long as they share some of their research results.
Or, to put it another way; Vulcan High Command has managed to foist off the boring administration work onto the humans, in exchange for mere unimportant status, and is not eager to have it land back on their laps again.
Of course, some Vulcans do think that a Vulcan-led empire would be an improvement over a human-led one. The last batch to think that went off and formed the Romulan Empire. The Vulcans and the Romulans are currently running a long-term, large-scale experiment to see which paradigm creates a more lasting empire in practice. (They don't tell the other races that it's all a political experiment, of course. They might not be great at interpersonal realtions, but they have found out in the past that that is a very bad idea).
It's not mere unimportant status, though. The Federation makes decisions that affect the state of the Galaxy, and they make different decisions than they would under Vulcan control, and those differences cash out in terms of significant differences in overall utility. For a culture that believes that "the fate of the many outweighs the fate of the few, or the one," the choice to allow that just so they can be left alone seems bizarre.
Of course, that assumes that they consider non-Vulcans to be part of "the many." Now that I think about it, there's no particular reason to believe that's a commonly held Vulcan value/belief.
Here's another installment of rationality quotes. The usual rules apply: