The reason why God doesn't want to wipe your past completely out of your memory is because He wants to use that part of your life for the work He has called you to do. He can take the worst thing about your past and make it to be part of greatest blessing in the future. He will weave it into the foundation of your ministry to the world, and out of it you will bring the life of the Lord to the other people.
That's why God want you to learn from the past and witness firsthand how He can redeem it, He doesn't want you living there. He wants you to read your past like a history book, not like a prophecy for your future. He wants you to forget those things that are behind you and reach toward to those things which are ahead. (Philippians 3:13)
Many people never get to the future God has for them because they are perpetually stuck in the past. A good example of this are people who have experienced rejection in their past and still fear being rejected now. They expect to be rejected, so they read rejection into other people's words and actions. This causes them to always be hurt, afraid, angry or bitter, it makes them oversensitive to other people's comments. In other words, their fear of rejection causes the very rejection they feared. It becomes an endless cycle.
Whatever weight from the past you are carrying will be observed by others, even if they don't know what it is. The bad things that happened to us, or the good things that didn't happen to us, will be part of what we wear daily and people will see the total look even if they can't recall the specific details. But God will deliver you from you past and He will use it for His glory if you ask Him to.
Excerpt from Power of a Praying Woman p245