If He chooses, then there is no such thing as Free will and there would be no point to Him becoming man.
John 6:44-45 "No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day. It is written in the Prophets: `They will all be taught by God.' Everyone who listens to the Father and learns from him comes to me.
The keyword is draw, not pick. Also, "they will all be taught by God". Note He mentions the choice of listening and choosing to draw near.
Must the spirit be quickened in order to discern spiritual versus carnal?
How can flesh discern that which is spiritual? If, as the Word teaches us, that we are all born spiritually dead, Who gives that spirit life so that it can see?
Since man does not have the power to quicken the spirit, which is dead from birth, then there is no way that it can choose anything.
Therefore, He chooses us, and we are unable to choose Him.