Why do we seek to be indepedent of asking anyone for help?
Pride. Control issues. Selfishness. I think mostly it's just plain old sinful pride.
Why do we seek to be independent of God?
I believe this is really a faith issue. I think we lack faith in God to really take care of our problems. Not only do we think we know what's best for us, we don't have the faith required to trust Him to know better.
Why should we ask God to give us daily bread so long as we can earn a living for ourselves?
For me, it has to be to help me develop a "helpless" attitude. It will instill in me an mindset that God is sovereign and without Him....nothing. It helps me focus that He is in control and that apart from Him, I can do nothing.