"It was my eyes that read these words but my soul that knew their meaning." Augustine, Confessions, IX.4
Proof-texting occurs when we look for words that back up our pre-formed conclusions. It happens in religion, of course, all the time. It happens in politics - pay attention to the ads that will play during the upcoming election year, and you'll hear quotes from the candidates that, while accurate, are misleading as to what they were really saying. "You took me out of context," the aggrieved party will rightfully say.
I can't help but think that God says that to us several million times a day. "You took me out of context." Now, don't take me out of context. I do believe that the Bible is God-breathed, that we can trust it fully, and that God's promises apply to us today. But I don't believe that our interpretations and conclusions are equally God-breathed.
I'm all for memorizing individual Scripture verses and studying individual verses, passages, or chapters. I do it regularly. But in the midst of all this, we need to seek out the heart of God and the logic of God behind the words.
For example, there's a verse that says I can divorce my spouse if he/she commits adultery. But what's God's heart behind the matter? I could probably find some verse to support whatever position I have about immigration policy, but what does God really think about how we treat the "foreigner" and protect our jobs, etc.?
"He made known his ways to Moses, his deeds to the people of Israel" (Psalm 103.7). It's good to know what God has done. It's even better when we know why He did it [though not everything will be revealed or even comprehensible to us, of course - "The secret things belong to the Lord our God, but the things revealed belong to us and to our children forever" (Deut. 29.29)].
"'For my thoughts are not your thoughts, neither are your ways my ways,' declares the Lord. 'As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts'" (Isaiah 55.8). We need to learn His ways and His thoughts. This can only come as we steep ourselves in His word (all of it, not just the favorite passages) and ask him to form us through prayer. The Bible is not a reference book, and God is not the "answer man." It's too deep, too rich for all that.
"The Bible says..."? Sure. But what does God mean? As with Augustine, our eyes must read, but our soul must learn.