“Allowing Jesus to save you does not make you your own savior”
Sure it does because it gives you the final say-so in determining whether or not you are saved. God becomes passive, waiting for men to make up their minds.
God draws all men to Himself and wants for none to perish but for all to repent. Ultimately, we have the choice to accept or reject his payment for our sins. That payment was death on the cross, not our faith in him. We are saved by faith because He died for us. It seems like you are playing word games. Having the final say does not equal dying on the cross and therefore doesn't equal saving ourselves.
It means you are smart enough and wise enough and pious enough to know the worth of the gift and the depth of your own insufficiency. But the natural man does not possess the ability to know those things. Only the spiritual man can know the things of God, can feel true sorrow of his sins and repent of them, and this ability occurs after that man has been reborn by the Holy Spirit, according to the will and purpose of God, and not according to men's own running or willing.
No it means that we have free will. God draws us to himself but we can decide to reject Him. Why is it so hard to believe that God would give us free will? That for His glory, we can chose to follow Him?
Free will means that the actual names that wind up in the Book of Life will be determined by chance. Some will choose, some won't. How does an omnipotent God leaving the eternal salvation or not of His most beloved creation up to utter chance glorify Him? True glory to God would be for ALL of His children to be with Him for eternity according to His accomplishment of His own perfect plan. Random chance cannot play a role in glory going to God. It would make no sense. Is deserved glory ever gained by accident?