In old days to be unteachable was to refuse to listen to what was being taught, even if it was the truth.
Now a new and far more pernicious form has taken its place. Ironically it parades under the guise of teachability. It is the unteachableness of universal acceptance. It is the unteachableness that never actually seeks truth at all, simply desiring to please every man by acknowledging that some part of what that person taught is probably true.
Instead of being firmly convinced of a wrong idea as truth, this new unteachableness rejects the heart of truth, accepting everything as true.
If one person teaches something one week in sunday school and the exact opposite is taught the next week, both are true. If one sacrament talk teaches one thing and the following speaker teaches the opposite both are true. The only exception is if the second speaker openly acknowledges that he is contradicting the first, in which case we want to assume he is wrong because that was such a rude thing to do.
This deviant abandonment of our quest for truth is not outside what is found in the scriptures. It is found among the greeks Paul taught who erected a statue to "the unknown God". By worshiping every God that was presented, and even the ones they had never heard of, they thought to please God. They abandoned the search for truth in favor of an ever growing checklist of meaningless possibilities.
We think we are teachable when we will accept any idea. The vast bulk of our members have come to a point where they will claim to accept two directly contradictory ideas as both being true without batting an eye. We no longer search for truth. We think it is enough to simply belong to the true church. Our membership, not our knowledge of our Father and our God, is apparently all that counts with us.
We have come to the point where it is counted charity among us to fail to reject falsehood. But we cannot gain truth without rejecting error.
Sure, like the greeks, we can have our statue to the unknown God. We can content ourselves with the false idea that as long as we pay some devotion to truth then having accepted an even larger measure of error is of no consequence.
But this isn't teachablity, it is a pernicious form of unteachability. I think it harder to repent of this form of unteachability than it is to repent of more traditional hard heartedness. The cynics heart, in time, may melt under the right occasion, and the doors may to truth may swing open within him. But teaching the relativist is like pouring water into a sieve. Even if some circumstance brings them to themselves, the next day no change endures. It is all lumped back into the melting pot.
When I was younger my Father told me about teaching the gospel to Shinto believers. They, like the Greeks of old, believe in a large number of Gods. They claimed to accept the missionaries teachings with relative ease. But they exhibited the same unteachableness as the Greeks. Acceptance of a little truth is meaningless without rejection of a vast amount of error. Once the truth is simply floudering among a hundred competing ideas without error ever being rejected as false then the search for truth is dead.
When we become like the greeks who want to accept everything as true, then we aren't seeking the truth. We are simply rationalizing away our days of opportunity.
The greeks accepted every possibility lest they offend some unknown God. But we have turned to accepting every possibility lest we offend a mere man.
The search to acknowledge everything as true is destructive to the search for truth. It destroys the integrity of truth. It destroys the integrity of the seeker. It is poisonous to the very nature of truth. It is putting our desire to please everyone above our desire to know our God.