ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ)
He's spent his life devoted to the idea that asking questions, and encouraging others to do the same, would make himself, his students, and the world a better place.
He died for that idea.
People aren't dying today (in most places) for this same idea, but they are often silenced. Socrates challenged the standards of everything and held that nothing could be beyond examination. Religion, politics, love, science, warfare, history - all of it was fair game. And, like it was 2,400 years ago, all of it still strikes a nerve when anyone seeks to question the decided truth.
Doubt is tantamount to heresy in most churches, in most political parties, in most relationships, in most of our lives.
Yet doubt guides us to truth. Doubt gives us the tools and the distance to learn. If we don't doubt our own knowledge, we can't add to it. If we don't doubt our own conclusions, we can't better them. Without doubt, progress is impossible.
If the conclusions you've come to are right, then there is no risk in re-examining them. You will, invariably, discover that they are still correct. So, the only risk to examining your long-held conclusions is that you might be wrong. The only risk is that you might find an erroneous conclusion that you can change.
That risk was so terrifying to the people in power that they put Socrates on trial for it. He chose death rather than living a feckless, risk-free life with no more examination.
How do you deal with doubts?