How can recognizing our weakness, though painful, bring us to know God?

Recognizing our weaknesses brings humility.

And if men come unto me I will show unto them their weakness. I give unto men weakness that they may be humble; and my grace is sufficient for all men that humble themselves before me; for if they humble themselves before me, and have faith in me, then will I make weak things become strong unto them.

Ether 12:27

When we recognize our weakness and powerlessness, then we can more fully understand how much we need the power of God. We give place for the Atonement and recognize our need for grace.
If we ask for help and reach out to God, then that means we are asking Him to remove our shortcomings, but that is Step 7. This is Step 6 -- to become WILLING or ENTIRELY READY. That's all. We just have to get our hearts in the right place and DESIRE to have God remove our weaknesses. 

But this is only one part of the request. The follow-up is that He will replace our weaknesses. If we want to give up OUR weaknesses, then that means we want to gain HIS character traits instead. We put OFF the natural man and put ON Christ's nature. We have divinity in us too, so we are by nature drawn to the divinity of Christ. While we are apart, we will always experience some level of "divine discontent" as Neal A. Maxwell called it. A longing to be better than we are and to be reunited with Christ & Heavenly Father.

STEP SIX

Al-Anon/Alateen:
Were entirely ready to have God remove all these defects of character.

Healing Through Christ Foundation:
Become entirely ready to have God remove all our character weaknesses.

(The title of this post is a question from the Healing Through Christ Family Support Workbook p.62.)