A man that was drowning does not boast in his belief that the life guard could save him and that is why he stretched forth his hand. He boasts in his savior, not in his God given ability to stretch forth his hand and be saved. His eyes are not on himself, his boast is not that he believed. His boast is one of gratitude for being saved.
As for faith, it cometh by hearing and hearing by the word of God. It cometh, as one is awakened if you will to the facts (the truth). It is not as if God has put faith in a concoction and poured it into a bottle to drip into the mouths of those He wishes to save. His desire to save all contradicts with your premise of election, and that Christ died for all also opposes your idea of faith and salvation.
We are not God's slaves, robotic creatures only believing because He has deemed it so by injecting faith into us. What pleasure is it for God to have a man believe if the man's belief is simply instilled by God? That is like drawing a masterpiece and praising your son for his work, illogical.