There are two ways to be unteachable.  The first is to be presented with some sort of teaching and to reject it or harden your heart towards it in some fashion.  The second is to avoid putting yourself in positions where you hear new teaching or are challenged at all.

If you’re going to be unteachable (which is not advisable) the first way is actually better.  It’s better because something might eventually connect with you or inspire you, either now or down the road.  You might reject something at first only to turn around and agree with it later.  At some point, it might just take root in you and start to bear fruit.

The second way, however, is very dangerous.  It’s a more subtle form of pride with disastrous results because you’re never actually exposed to anything to begin with.  On the surface this keeps everything nice and polite because you don’t seem to be rejecting anything but the truth is that it’s worse because you’re rejecting things before you’ve even heard them.  You’re unteachable from a distance.  You’re not just refusing the teaching.  You’re doing something far worse.  You’re refusing to hear.

Are you avoiding new ideas or new challenges that God wants to bring into your life?  Are you teachable?