Of course, too much doubt can be paralyzing. If we are afraid about every step we take and overanalyze potential failures, we will not get too far. However, when we are not able to take a critical look at our beliefs and actions, we won't see our mistakes, and won't adjust to changing circumstances of our lives.
It's not a coincidence that the scientific approach to understanding the world (as opposed to art or faith) is based on doubt. Good scientists question their beliefs all the time, and change conclusions of their research based on available data. (This principle does not always work in practice, but this is how science ideally should be).
When we are convinced that we are always right, and ignore alternative opinions, it is not a sign of strength but of weakness. It means that even if we are wrong (and sometimes we surely are) we won't be able to notice or admit it.
So what does having a healthy amount of self-doubt mean? We should be able to ask ourselves once in a while: Why do I believe what I believe? Why do I feel what I feel? Why do I act the way I act? We should not be afraid to admit our mistakes and biases. Nobody knows everything, but everybody knows something, so it is crucial to listen to others, even when their opinions seem to be different from ours.
Doubt is not something to fight against. It is essential for being human, for evolving and understanding the complexity of the world.