Turning our thinking on its head is an unsettling experience. It's hard to admit we always thought wrongly about something. And it's not easy to see the subtle nuances where a new way of thinking has to hold different truths in tension.
Here's an example:
Most people today believe that they are sin-free and sinful. What's wrong with that? A renewed mind that thinks differently by the Spirit begins to realize that is is not a matter of being sin-free and sinful; in reality we are sinful and sin-free. Let me explain.
The common view of reality is that we are all basically good people. To describe people as sinners is deeply offensive. In fact, the idea of committing sins hardly appears in our vocabulary. Perhaps we make poor choices, perhaps we have certain conditions that cause us to behave in inappropriate ways. But few people think in terms of committing sins. Theirs, by definition, is a sin-free fantasy world. However, ironically, many people are nonetheless plagued with a sense of guilt or shame. Their sin-free reality where sins have been redefined out of existence is still filled with feelings of sinfulness.
As we begin to understand the truth about the world and ourselves in Christ, it dawns on us that we are not inherently good people. At the core of our being is a sinful nature out of which flows all kinds of deeds that really are sins for which we are morally responsible. "Oh wretched man that I am!" cried Paul (Romans 7:24), as this transformed self-righteous Jew who once thought he could do no wrong realized the depth of his former delusion.
And yet, as the light of the Gospel sinks in, we begin to realize that all those things which plagued us with a sense of guilt and shame, things that we can now acknowledge to be sins, have all been placed on Christ. In his death he has removed our transgressions as far as the east is from the west and we have truly become a sin-free zone by God's reckoning. "There is now therefore no condemnation for those who are in Christ Jesus!" exclaimed Paul just two verses later, before the ink had dried where he penned his earlier cry. He knew he was sinful and sin-free!
Dietrich Bonhoeffer describes what this renewed thinking looks like in a Christian, in a believer who mind has been turned right side up. According to Bonhoeffer, such a person
...knows that God's Word in Jesus Christ pronounces him guilty even when he does not feel his guilt, and God's Word in Jesus Christ pronounces him not guilty and righteous, even when he does not feel that he is righteous at all. [Life Together, p.22]
Only the Holy Spirit can help us get our minds around this. But when he does, everything changes.