How many times have I heard that verse? In case you are wondering, it refers to Proverbs 3:5
"Trust in the Lord with all your heart, and do not rely on your own insight. 6In all your ways acknowledge him, and he will make straight your paths. 7Do not be wise in your own eyes; fear the Lord, and turn away from evil. 8It will be a healing for your flesh and a refreshment for your body."
The reason I bring it up is because it has been used in many instances to keep people from thinking too much about the Bible. The logic is that by thinking too much on what it says, you are ignoring what God is telling you. I hear it most often when I am arguing with a fundangelical about things like inclusion of LGBT men and women or not taking the Bible literally.
But looking at the passage a little closer, I don't think it is saying not to use your God given reason to study the scriptures. Far from it. I think it is reminding us that when we do seek Wisdom, it should be prayerfully, in a conversation with God. It is about trusting in God's Wisdom and not what you think you know. When we think we know something, we become blinded to the other ways of seeing things. This pride is what the Teacher warns about. Ignoring God because we know it all.
So many times people, especially biblical literalist, will read a passage or two in the Bible and attach a meaning to it, then never go back and revise that. They are relying on what they think it meant when they read it before, or what they heard their pastor say it meant. So we "understand" that it means this one thing. However, when we take those blinders off, stop relying on what we "understand" of the scripture, and let the Holy Spirit show us a new way to see it, the Bible again comes alive!
God does not want mindless robots. He wants willing servants; people who desire above all else to know Him and to love Him. When we clamp our Christianity into one way of seeing, we stop growing and become spiritually dead. This is one way of looking at the teaching in Proverbs. Don't rely on what you think you know, but seek Wisdom. Allow God to change the lens through which you see Him. Open yourself to the possibility that you may be wrong.