When you think of the phrase "get wisdom", does it conjure up times when you were taught by someone that actually had wisdom? It's beyond difficult to get wisdom from anyone other than a wise person. The trouble with the world today is that there are far too many people who think they are wise...teaching people that believe pretty much anything they hear. What a sad scenario.
Being teachable does not mean that you are gullible, it just means that you are wise enough to know who you should be learning from and who is just full of themselves. Being teachable is being open to new ideas as long as they don't contradict God's ideas and precepts. You will be sure that when false teachers appear, you recognize them and don't allow that type of deception in your life. Being teachable also means that you are ready and willing to pass the wisdom that you have gained on to those that need it.
Having a humble spirit and being willing to admit your mistakes while making corrections is important in someone that is teachable. You have to be willing to admit that you are wrong when you are and allow the fruits of the Spirit to be a part of your life.
Being teachable brings wisdom and wisdom needs to be shared with those who are teachable. And so the circle of teachability goes on and on.