I "Am Very Open-minded"

I think Chesterton's implication is that the problem is with the mind that, like his example of the open mouth, remains open and slack, rather than "closing on" (or, to extend the metaphor, chewing over) "something solid." It is true that a permamently closed mouth admits no food! But a vacuously open mind, like a vacuously open mouth, admits much more than worthwhile nourishment. :-)