"A Mystery, in short, is an invitation to the mind. For it means that there is an inexhaustible well of Truth from which the mind can drink and drink again in the certainty that the well will never run dry, that there will always be water for the mind's thirst." - Frank Sheed
This is a reassurance that when we fail to wrap our puny brains around a mystery, we are fundamentally incapable of full knowledge, of "getting it completely." We are encouraged not to despair at it but to continue trying. To put on the mind of Christ.
And how "anti-modern" is that reassurance? The mind of materialism wants to believe that we CAN reach the bottom of the well. A "mystery" by that definition offends them. They don't WANT there to be something about which they cannot fully know, dissect, understand down to the bottom. There is no room for a transcendent God who is not fully knowable and so must be excluded.